Godmother
Well-Known Member
so many of us have struggled with guilt when our ratties have gone from apparently healthy to dead in a couple of days, or even hours. We always wonder why we didn't notice something sooner.
The only way I can get my head around it is to think about how, in two of the common causes of death, exponential growth of bacteria or cancer cells is involved.
With exponential growth, the increase in the deadly cells is not apparent until things are near the end. For an example of exponential growth, remember the example of saving one penny on day 1, doubling it every day, and seeing the growth pattern. At first, the amount is very small, then suddenly it's huge.
I believe that bacterial growth and some cancer growth is like that. Here is a web site with a great illustration:
http://www.worldpopulationbalance.org/p ... /1100.html
See how things change in just one minute at the end ... http://www.worldpopulationbalance.org/p ... /1159.html
If we could only see that something was wrong early on, then maybe we could treat it in time. Problem is, the problem is invisible until it is too late.
Here's another web site with a great illustration of the problem: http://www.mathwarehouse.com/exponentia ... tivity.php
I also found this tidbit of information on Wikipedia. Human beings are built to perceive exponential growth as if it were linear (so it's hard for us to see what's happening):
The only way I can get my head around it is to think about how, in two of the common causes of death, exponential growth of bacteria or cancer cells is involved.
With exponential growth, the increase in the deadly cells is not apparent until things are near the end. For an example of exponential growth, remember the example of saving one penny on day 1, doubling it every day, and seeing the growth pattern. At first, the amount is very small, then suddenly it's huge.
I believe that bacterial growth and some cancer growth is like that. Here is a web site with a great illustration:
http://www.worldpopulationbalance.org/p ... /1100.html
See how things change in just one minute at the end ... http://www.worldpopulationbalance.org/p ... /1159.html
If we could only see that something was wrong early on, then maybe we could treat it in time. Problem is, the problem is invisible until it is too late.
Here's another web site with a great illustration of the problem: http://www.mathwarehouse.com/exponentia ... tivity.php
I also found this tidbit of information on Wikipedia. Human beings are built to perceive exponential growth as if it were linear (so it's hard for us to see what's happening):
Hope this helps.Examples of exponential growth
Biology.
Microorganisms in a culture dish will grow exponentially, after the first microorganism appears and a lag phase, and until an essential nutrient is exhausted.
A virus (SARS, West Nile, smallpox) of sufficient infectivity (k > 0) will spread exponentially at first, if no artificial immunization is available. Each infected person can infect multiple new people.
Human population, if the number of births and deaths per person per year were to remain at current levels (but also see logistic growth).
Many responses of living beings to stimuli, including human perception, are logarithmic responses, which are the inverse of exponential responses; the loudness and frequency of sound are perceived logarithmically, even with very faint stimulus, within the limits of perception. This is the reason that exponentially increasing the brightness of visual stimuli is perceived by humans as a linear increase, rather than an exponential increase. This has survival value. Generally it is important for the organisms to respond to stimuli in a wide range of levels, from very low levels, to very high levels, while the accuracy of the estimation of differences at high levels of stimulus is much less important for survival.