Monday, January 09, 2006

Positive/negative feedback loops in natural processes

Positive/negative feedback loops that occur in nature fascinate me. So I started looking for them and collecting such phenomena. I'm not 100% sure if some of these are really due to the presence of positive/negative feedback loops -- so take it with a pinch of salt.

In simple terms, a positive feedback loop makes a thing larger and larger until a breaking point. The larger it gets, its tendency to get larger increases. The reverse of getting continuously smaller can also be the result of a positive feedback.

A negative feedback tends to resist a thing's current course of change. If it is growing, a negative feedback till tend to pull it back. So growing more becomes harder and harder as the thing grows big. Hence a negative feedback system normally has an equilibrium point. Any big swing away from the equilibrium will tend to pull the system back into its equilibrium.

Mathematically positive/negative feedback loop systems can be described as below. Note that I may not be 100% correct here. Let the thing that is growing/shrinking be y. If dy/dx is a polynomial in x and has a degree >= 1 (or <= -1 for shrinking positive feedback), we can say there is a positive feedback. In simpler terms, the rate at which the thing increases is directly proportional to the current size of the thing. Probably a more accurate description is that, the change in the thing (rather than the rate of change) is directly proportional to its current size. Imagine a forest fire. Larger the forest fire gets, the more rapidly it spreads. So we can say this is a case of positive feedback loop at work. I couldn't exactly quantify what x is; but intuitively it is something whose little change can dramatically affect y's change as y gets larger. Usually most spectacular phenomena (like a stock market boom/bust, current fashion craze) would have a positive feedback loop working for it. Here is a list of feedback loops I collected. I'll update as I come across interesting cases.

Positive Loops:

  1. Nuclear chain reaction, nuclear explosion
  2. Hurricane formation
  3. The growing crowd at a road side accident site. More watching people attract still more people. The reverse is also true -- a shrinking crowd, shrinks faster. As more people leave, it becomes less of a crowd puller.
  4. Anger bursts. This I read somewhere; the way human anger response works. Once it gets started, it keeps growing until it reaches a maximum point. I, for one, would bet on that theory having had first hand experiences :).
  5. Investment growth using compounding returns. Think of the growth of an initial investment in 401k over say 30 years.
  6. Popularity of already successful books/shows/ideas/etc. Usually people talk about book sales "taking off" or reaching "critical mass". It is when the book makes it to the top sellers list. I think this is a classic case of starting off of the positive feedback loop. There is no stopping of the runaway success.
  7. pumping and dumping of penny stocks. It is similar to the above case of book reaching the top seller list. Once a stock has been artificially pumped up (by a select few), others jump in pushing it further up. Again a start of a positive feedback loop.
  8. Stock market/ Real estate bubble build up. The reverse burst. Once an asset is seen growing more, more people want it. Higher demand drives value up. Again a start of a positive feedback loop. A crash in prices too gets into a positive feedback loop -- though here the effect is in making the value smaller and smaller.
  9. Trust/emotion building among people/groups. Includes cases of trust, love, hatred.
  10. Growth of a monopoly. Take Microsoft in late 80's, early 90's; or Walmart. In Microsoft, the explosive growth of windows can be seen as a result of positive feedback loop at work -- more apps for windows leads to more windows adoption. That triggers more developers to produce apps for windows (instead to say Linux or someother platform).
  11. Formation of black holes. More mass leads to heavier gravitational pull -- leading to more attraction of other mass. A cycle is established. It is an interesting comparison to see the way a monopoly works with this sucking effect of a black hole. Lets consider the introduction of a Walmart superstore in a community. It just sucks up all the mom-n-pop businesses and that leads to attracting their customers. Walmart just grows bigger in sales; now ready to swallow bigger guys -- I think the fall of Levis, RCA, rubbermaid to walmart can be seen as instances of such big guys falling.
  12. Population growth of self-reproducing entities. Includes all living things, computer virus, successful memes (like religion). For living things some examples are rabbit population, water hyacinth growth in a lake, cancer proliferation, biological epidemics (flu virus spread). The spread of successful ideas (memes) also employ positive feedback loops. More people exposed to an idea increases the chances of the idea spreading more rapidly. I guess gossips/rumors are a good example.
  13. Economic boom/depression. Similar to the stock market boom. More activity creates more jobs and a cycle gets established. The reverse happens in an economic downturn.
  14. Technology adoption. More technology adoption feeds innovation, leading to birth of newer smarter technology. Growth of Internet is an example.
  15. Drug addiction. Cocaine mimics the naturally occurring happiness hormone endorphin. On drug intake, the brain sees a sudden flood of endorphin like substance and shuts down the endorphin receptors. When the drug is digested, the person can no longer feel good since the naturally occurring endorphin is not sufficient enought to plug on to the available open receptors. He takes in more drug to achieve a prior state of well-being. That triggers closing down of still more receptors and reduces the available open ones. There starts the vicious cycle.
  16. Becoming obese: It's lot easier for an overweight person to add on more pounds -- bigger body demands more food. It also results in lesser exercise/physical activity. Both can setup a cycle. The good part is losing weight can also exploit the workings of a positive feedback loop. Once a few pounds are lost, it may need lesser effort to reduce further. There are many unknowns here and I may be off the mark.
Negative Loops:
  1. The classic spring example. It takes more and more effort to press/expand a spring from its natural equilibrium position.
  2. Steam power control in old steam locomotives. A valve opens/closes to regulate steam output based on the current steam power output. More power reduces the valve leading to power reduction. Less power opens up the value to increase power.
  3. Predator prey population. Think of lion-deer population. More lions implies reduction in deer population; that implies starvation for lions. This leads to an equilibrium state. Less lions implies population growth for deer leading to more food for lions helping their growth.
  4. Classic case of price stability due to supply-demand balance. Lets take oil price increase. Higher cost drives demand low (due to less driving, say) and that pulls back the price to an equilibrium state. The reverse happens when oil prices drop.
  5. Human body homeostasis. The body tries to maintain an equilibrium; lets take temperature. If too cold, the body shivers to bring up the temperature. If too warm, the body evaporates to cool down.


At 7:32 PM, Blogger Anbae said...

Hai Karthik, this post s simply amazing.. excellent... A simple thing had its full long satisfied descriptive explanations by ur shapend views.. Wow, it's really intresting Karthick, Mathematics + science --> Mathematical-science together explaining the real phrase's theme,hmmmmmm vividfull.. thankx u ..i liked this view,,,

Me, a starter stepped in to this blogger world just to pick up my worthless worst english to the better side with vocabulary sensed communication.. me, surfing sites and homepages, only to cultivate my mind to feed something with thier words and vocabularies ..only upto my stupit targets.. i'm not bookish either.. But interests in blogging picked me here.... don know.... im impresseed with ur words.. just like a addict hereafter i ll check ur page daily.. thankx u...

It's the third time to ur page but im thinking tht im so late to pick this page.. simply impressed with this post sir, with ur explaning words explaining to structure out things together with the experienced views.. hmmmmm, inshort these are pridefull pendown scripts.. really gr8.. like to add u in my link list, can I?

At 9:44 AM, Anonymous Anitha said...

Hi Karthik,

Came to know about ur blog thru Priya’s.. was pleasantly surprised.. “heat/cool car” and “outsource driving” made an interesting read..

continue blogging.. would love to get more posts from u..

And enjoy ur vacation in India.. see u in Feb

Have fun

At 11:48 AM, Blogger Karthik Gurusamy said...

Hi anbae,

I'm happy you like the post. Appreciate the kind remarks. It's true that any reading is going to do good; blogging isn't an exception. But I used to think there is too much substandard stuff on the net which can take up your time. Nothing beats a good book though. I use to say, net surfing by jumping from page to page is like eating junk food. Reading a good book is like eating a whole healthy meal.. and we all know which is best! and yes a little bit of junk food doesn't harm either ;) BTW I'll be away for a month on vacation and will continue to post once I'm back in Mid Feb.

At 11:50 AM, Blogger Karthik Gurusamy said...

Hi Anitha,

Welcome to my blog :) I just started very recently... hope you like the posts. Will try to add good ones as it occurs. See you guys back after I return from vacation in Feb.

At 6:44 PM, Blogger Jagan said...

Thats a long post ...I landed here by blog hopping .I have read half the post and will complete reading the rest later ..thought I will end with a "i was here " comment :-) ... too into networking we we are "same kuttai le oorna mattai" :)

At 1:30 AM, Anonymous hgh said...

can i get more info?

At 6:23 AM, Blogger Karthik Gurusamy said...

Hi Jagan,

welcome to my blog.. I'm away right now on vacation and will add more posts later in Feb.. do visit back

Hi hgh,

Welcome to my blog..I've a few more examples (e.g. herd behavior, explosions, domino effect, progressive collapse of buildings) and a short description which I plan to add once I'm back from vacation. Right now I'm in India and sitting behind a very slow dialup.. do check back by end of Feb.

BTW let me know if you have anything specific in mind..


At 1:29 PM, Anonymous Megan said...

Hi Karthik,
I found your post when doing a homework assignment dealing with positive/negative feedback. I was confused, but your post helped clear things up. I found your post very helpful and thank you for the assistance that I needed. I also read one of your replys to another comment about how a book is like eating a whole, good, and health meal. I agree completly because nothing beats a good book. Good work on yout post and thanks again.
(Could I learn more about your examples on domino effect and herd behavior?)

At 2:28 PM, Blogger Karthik Gurusamy said...

Hi Megan,

Thanks for the comment. Good to know the post was useful to you.

About the domino/herd behavior:

Both involve positive-feedback loops.
In plain English people use terms like 'chain reaction', 'snow-balling', 'vicious cycle' when the underlying process is being driven by a positive feed back loop.

For domino, the familiar example is a falling of a series of cards. Once the fall starts, the load on a future card is more and hence easier to topple. Thus rapidly all cards fall. It's similar to progressive collapse of a building. In this case, a multi-story building collapses when the top few floors collapse. This builds more strain on the next standing floor which brings it down a little more easily. Thus once the top floor collapse starts, it's far difficult to stop the complete collapse (similar to the 9/11 WTC building collapse)

About herd behavior:

When people copy behavior, the behavior spreads rapidly. One interesting thing I observed is on an air-plane landing -- how passengers stand up to pick up their checkin baggage from overhead cabins. Initially everyone is waiting if it's okay to start; the moment one or two people begin to stand, within a few seconds almost everyone is doing the same.

At 10:05 AM, Anonymous Megan said...

Hi Karthik,
Thanks for the further info it helped clear things up even more for me. Keep on doing what you do.

I think that another example of a domino effect could be the human population. The more that it grows the more strain it puts on the earth's resources that we all rely on. Hopefully we don't topple. But I do think this is very simmilar to what you said. Please let me know if I'm anywhere near the mark. Thanks.

At 3:38 PM, Blogger Karthik Gurusamy said...

Hi Megan,

If you consider human population growth as a self-reproducing entity, yes it's an example of positive feed back loop. And hence similar to domino effect.

But if strain on resources is considered, we will be talking about negative feedback loop. This is very similar to predator-prey population.. too much predator, implies starvation to them and hence the predator growth slows down. Thus too much a human population will hit resource starvation leading to slow down in growth.

It's interesting to see the same population growth can under-go positive feedback loop at times and when it's over-done negative feedback loop kicks in. Hope that helps.


At 9:40 PM, Anonymous Anonymous said...

hi Karthik,
i am currently taking a biology class in which negative/positive feedback loops are the hot topic. i have a couple of questions, if you don't mind providing your input: how might a negative feedback loop explain why people who lose large amounts of weight gain that weight back? Do you think that weight in humans is regulated by a negative feedback loop?


At 1:29 PM, Blogger Karthik Gurusamy said...

Hi Krystle,

One of the accepted principles that regulate body functions is Homeostasis. You can read up on it in wikipedia; basically it is a method to bring down a quantity to a stable steady state quantity when it strays far from the steady-state value. One example is body-temperature. During cold weather, the body tries to bring the temperature up (say by shivering) or in hot weather, it sweats to increase evaporation/cooling.

My guess is people have a unique metabolic rate and losing a large amount of weight in a short period of time will trigger a response in the body. This is very much like a negative feedback loop where changes from a steady state is not encouraged. I am sure the reverse is true for a lean person to put on a lot of weight in a short time.

Hope that gives some ideas.


At 11:51 AM, Blogger joylucks said...

It is good to study the feedback loops in nature. It would be more useful to study the feedback loops in business though. All the best businesses in the world has great stable feedback loops. For example, Moody Corp has probably the best feedback loops, that is way Warren and Charley invested own 20% of the company

At 9:42 PM, Anonymous exam_studier101 said...

Could a negative example be body building? the bigger you get the harder it is to get even bigger?

At 11:12 AM, Blogger Karthik Gurusamy said...

exam_studier..'s a -ve feedback tries to bring the body wt to the normal state.. it's like a stretched spring..the more it's stretched ..the harder it becomes to stretch even more

At 11:02 AM, Blogger Yolanda Velasquez said...

Wow! This blog site really explained and helped me understand the difference between the positive and negative feedback loops. thanks



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