Calculating the Half Life of Awareness

1. MistyKe

4
This is a strange one, I know. I have background info below. Here is the question:

How would one begin to calculate the half life of awareness (the social and political)?
What would the equation to calculate that look like?

I am a grad student in art and am making work about social issues, namely e-waste dumped in developing countries. I'm trying to work basic science facts into the thesis to make the work more complex and engaging, mostly regarding the half life of the components found in electronics. But I am interested in the decay factors that create apathy or cause us to forget after we have awareness on a specific topic. Are the factors around this half life based on how active your outside world is, the level of exposure to advertising, one's level of personal wealth?

I realize this is really a question in poetics, but would love to hear a physicists' thoughts and I realize the answering theories would be nothing but speculation. I think this is a perfect place for science and art to intersect.

2. Math Is Hard

4,915
Staff Emeritus
Hi Misty,
This looks like more of a social science question so I am moving it to our social science area. I'm not sure there's really a way to "model" this phenomenon the way you might be expecting, but we'll see!

3. MistyKe

4
Great. Thanks for putting it in a more appropriate forum. I am looking forward to seeing responses!

4. CRGreathouse

3,682
I'm not sure why you assume that there is a half-life -- that awareness decays by a fixed percentage for every unit of time. Or if that wasn't what you meant, would you clarify?

If you do want a mathematical model I would suggest logistic rather than exponential.

5. MistyKe

4
So I have to admit my scientific language is limited. But I figured half life made the most sense. I'm thinking about awareness around different difficult social issues and how it fades out of your head. It doesn't turn into unawareness per se, it just fades from your mind. For example, if you see an incredible documentary on the war in the Congo and it really stays with you for a few days. How would you calculate the time it takes for that to be completely out of your mind, something you do not contemplate anymore?

6. CRGreathouse

3,682
If there is a half-life for awareness then the knowledge never completely leaves, just fades to an arbitrarily small percentage of original awareness.

7. symbolipoint

3,070
Interesting question but imprecise. An advanced student of Sociology might be able to give a sensible discussion about how to design a model for "half life of awareness". Sociology degrees (at least starting with undergraduate) would at the very minimum require "College Algebra" and elementary statistics courses. One would imagine that polling would be needed and performed over several years. One would want to decide whether to sample randomly all people or ask the same exact group of people so no younger generations would enter this group being sampled.

Not a bad question. People more suitably educated and experienced should be able to give better responses.

8. maverick_starstrider

Personally I think looking for an equation, or speaking of the mathematical/physical notion of a half-life sounds like an attempt to manufacture the sense of quantitative understanding where none could ever exist (although I'm aware that people in social science love to do this all the time). Your first, and most important, step is to come up with a metric for awareness. I.e. you would need a way to quantify the amount of awareness a person has of something at a given moment. I believe in the social sciences something like a questionaire or survey would be in order. I suppose you could use as a test group everyone who saw the documentary and then everyday randomly chose 10% or something of the group and give them the test. Obviously you couldn't ask the same people twice because after they take a test on it they're going to be more aware of it then they normally would.

9. apeiron

2,432
Some interesting issues raised.

First key point would be that talk of half lives invokes a particular statistical distribution - a powerlaw decay. The alternative decay profile would be exponential. And so one would usually indicate a random process, like radioactive decay, that is equally likely to happen at any moment. The other would indicate a damped process where likelihood of decay increases with passing time.

So your "equation" could fit two quite different profiles - log/log vs log/normal. You would have to be making a correct choice. And the concept of a half-life would only really apply to a powerlaw (or Poisson) distribution of events.

Then you want to apply a random distribution to a complex situation like people's awareness of the e-pollution they export to poorer countries.

Complex sociology often does produce powerlaws - like Zipf's law, etc. And it is pretty much always when a system is freely expanding. So if true that there were some half-life to the degree that people maintain awareness of the e-pollution issue, you might then possibly be able to tie it to facts like the developing world seems a bottomless pit for Western junk. It is the freely expanding space that powerlaw outcomes demand.

So say the developing world fills up, or spills over toxically into our own. Free growth of pollution is now being globally constrained. Awareness is likely to switch from powerlaw forgetting to some new statistical profile - perhaps exponentially rising alarm as the pollution closes in!

The human mind and its memory banks also seem to be near infinite in capacity, another kind of bottomless pit. So you could argue that remembering and forgetting/ignoring would in general follow a powerlaw profile.

You could follow a hierarchical approach based on nearness to attention.

So central attentive focus at any one moment: capacity = one thing.

Working memory; capacity = 5 to 7 things close at hand.

Then longer term memory would be populated powerlaw perhaps by 50, 500, 5000, 50,000, etc things at increasing distance from immediate awareness.

Coming back to e-waste though, I hope you are not presuming that too enjoys a half-life of decay? I thought the problem was its failure to decay at any reasonable rate. And I suspect our production of it would have been exponential.

Last edited: Jul 2, 2009
10. CRGreathouse

3,682
??

Most e-waste is stable, with infinite half-life.

11. apeiron

2,432
As I said: I thought the problem was its failure to decay at any reasonable rate.

But sorry I missed your post where you already made the point about logistic vs exponential.

2,432
13. flatmaster

505
This is an interesting concept, but difficult to quantify. It would vary vastly on the individual. For example, I am a cyclist. Every chance I get, I hand out fliers and tell people about cycling events around Huntsville. I also hope to soon to be a part of Life cycles: a non-profit that fixes up used bikes for the homeless.
Someone else may have had a family member die of cancer, then suddenly become a cancer advocate. A mother may have an autistic child, they suddenly become an autism advocate. THis "half-life for awareness" is strongly dependent on an individuals life experiences.

P.S. I could care less about saving the manatee.

14. MistyKe

4
This is really great conversations. The social awareness (or lack of) in an audience has has been cited as a "problem" in documentary photography for the past couple of decades but this conversation in a more scientific setting is exciting. And it seems to me that flatmaster presents a catalyst to the equation - one's approximate distance (or intimacy) to the issue.

So considering the factors brought up in this forum, would a working equation (though not completely perfected or accurate) be possible?

15. flatmaster

505
I would say that all you could really quantify is that it decreases, and doesn't increase unless there's a stimulus or motivation of some kind to the particular issue. That's all you could really say. But heck, that eliminates many families of equations.

16. apeiron

2,432
Google "scalefree networks" for equations of this kind of phenomenon. Or "Barabasi". Or check this SciAm article...

http://www.nd.edu/~networks/Publica...leFree_Scientific Ameri 288, 60-69 (2003).pdf

Again, the one thing you need to know is whether the social activity of interest exists in a "freely expanding space". So the internet is the example of a free social space in that it is both vast and there is equal cost (roughly) for participating.

An enthusiasm for biking or whatever can take off (go viral) simply because enough people chose to respond.

The opposite story is if the social space is constrained, not freely expanding. So if there is a differential cost in getting involved, or some other boundary constraint. Different social dynamic models then apply.

Social dynamics is becoming a well studied field in its own right. But even scale free networks are a surprisingly recent story.

17. John Creighto

811
Wouldn't a scale free model more likely apply to what we retain rather then how long we retain it for. That is if ideas witch are closely related to other ideas of our interest then we are more likely to retain them.

18. John Creighto

811
I'm not sure if memory decays exponential or not but because linear systems are easy to work with then a linear decay model with a non linear output would be a simple way to describe the underlying dynamics.

That is we can describe the state of learning an idea in terms of short term, and long term reinforcement which is modeled by a linear differential equation.

Let

$$S$$ = short term reinforcement
$$L$$ = long term reinforcement
$$\lambda_S$$ be the forgetting rate for an idea reinforced in the short term
$$\lambda_L$$ be the forgetting rate for an idea reinforced in the long term
$$\beta_L$$ be the amount one review of the idea reinforces it in the long term
$$\beta_S$$ be the amount one review of the idea reinforces it in the short term
$$F$$ be the frequency at which the idea is encountered

Then one might propose the following simple model for idea/memory reinforcement

$$\dot{S} = -\lambda_S S + \beta_S F$$
$$\dot{L} = -\lambda_L L + \beta_L F$$

It is convenient to model the system without parameters which express coupling between S and L because most linear systems can be decoupled into independent modes though diagonialization of the state space matrix. Therefore coupling parameter would make the parameter set redundant.

Now how might we estimate our parameters? Well, first we need an output model to relate our reinforcement model to the probability of remembering something. For instance we could define the probabiliyt of remembering something as follows:

$$P_r=1-exp(-(S+L))$$

This equation is invertible. So we can calculate $$S+L$$ for a given $$P_r$$ without knowing any of the underlying paramaters of the above differential equation. One could try various reinforcements schemes and test the probability of remembering something with this scheme. This gives a value of S+L for each reinforcement scheme. Once S+L is estimated for several reinforcement schemes then the parameters that describe the underlying linear dynamics can be estimated.

As a final we may wish to also include some input dynamics. For instance $$F$$ for long term memory maybe be roughly the number of times the idea is encountered within a year. While, $$F$$ for short term memory maybe the the number of times the idea is encountered in a day. Many possibilities are available and we could represent these input dynamics as a linear or nonlinear filter.

Last edited: Jul 15, 2009
19. floppyflaps

1
I'm an undergrad in sociology and I've always been curious in mathematical models of human behaviour, but there's serious limitations to them.

Similar to other sciences, it's difficult to categorize exactly what information from what field(s) need to be used. To me, it seems like the best approach to this memory problem would be from a neuroscience perspective. Neuroscience is kind of an esoteric field to be quoting in your paper though. Not to mention such approximations would be completely nature, without any respect to nurture.

I'm sorry I can't help more, but such an endeavour would be tantamount to deriving an equation for all of human behaviour. An equation where you can input various variables, and have an output for the behaviour of what a person will do next. Specific theories, like game theory do a pretty good job at modelling the behaviour of what people should do in a conflict scenario, but it morphs into what people should do, rather than what they actually end up doing.

I'm sorry for not being much of help, so I'm going to give you a related concept that you can research. It's called narcotizing dysfunction, and it's relatively new research (maybe a decade old) into why people stop caring about things once they're given more information about the situation.

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