There is one water lily growing in a pond with a surface area of 130,000 square feet. In early spring, this lily has one pad, and each lily pad has a surface area of 1 square foot. After a week, the lily has two pads; after the following week four pads. After sixteen weeks the pond is half covered. How much longer will it take before the whole pond is covered assuming a constant rate?

What is going here?

Can one Y2K "glitch" be like a water lily in complex system of systems?

What does it mean?

3 day storm? Infomagic?

-- MarktheFart (quke@ix.netcom.com), July 16, 1999

Answers

One additional week -- the lily pads double in size weekly; the pond is already half-filled, hence, next week the lily pads double and the pond is full.

You're asking if there is a "critical mass" for y2k, at point at which the errors pile up and the descent toward Infomagic cannot be stopped.....

Let's hope not.

But prepare like there is....

Anita Evangelista

-- Anita Evangelista (ale@townsqr.com), July 16, 1999.

Well now I'm going to technically disagree with you there M'dear E.

Who could begin the initial flaws in the original poster - but who the h**l wants to talk to somebody with that handle rather than a lovely and talented Lousianaian?

One could in fact argue that unless the pads were rectangular or square and the pond also rectangular or square the pond could never be fully covered. This happens because there would remain gaps and holes between adjacent lily pads.

However, I am being picky and trivializing an important question.

Now - to the subject at hand: the spreading nature of lily pads in an unnamed pond. We shall, for simplicity, assume the lily pad is rectangular or square, rather than for example the more exotic diamond or club shape. We shall assume too that the pond is rectangular, and can therefore actually be covered by any given number of appropriately sized lily pads.

Any given lily pad that "doubles" in size must (per the original posting) double in either area (as a function of d^2) or in size (diameter). However, these lilies are not "growing" in size, (as they are said to maintain their constant 1 sq ft area) therefore they must be doubling the number of leaves present.

This assumption is in fact implied by the following geometric progression : ... has two pads, has four pads, ...

Now for the limiting physical condition this "doubling of number requires" - each "pad" must be exposed to the sun, and so can be assumed to be immediately butted up next its nearest neighbor. Each new pad is still attached to the same "root" system underwater - since only one "lily" is stated to be present. So, we can deduce that each new "set" of pads in the geometric series requires a longer and longer root (feeder stem) back to the remaining pads. (Or, if the central mass of the lily were "moving" sideways so as to maintain an "average" length of new connecting fibers to a "ring" of new pads, all of the new pads would require a successively longer stem back to the original center.) One could suppose that the new pads were appearing "next" to each original pad's original location (since two appear where only one was before), but then one would have to show how the orginal pads were being "pushed" further from their original position without getting their original stems "stretched" or broken.

However, this consistently longer stem would require successively more energy to grow and be nurished - and such new energy would also be increasing as the square root of the new area covered increased - more and more energy is required each week for the new wave of pads to appear.

Since no mechanism or regulatory mechanism is given to explain that why the new stems would be able to grow faster than the original stems, nor is there an explanation sufficient to explain why the original stem would have been restrained (not forcing the new pads in the center "up" out of the water), one must conclude the original question was not realistic.

Thus - what was missed in the original question is the "root accelerator " factor, or an external "root supression factor" needed to suprese excessive growth early on. It's absence can be used to show the orgininal question is misleading and distracting.

therefore, water lilies are not relevent.

Now, personally, I prefer the zebra mussel theory of hidden flaws that slowly creep in, infect a system over time but do not immediately cause massive failures; but which grow invisibly in the dark moist waters away from the light of truth, until they clog the system and nothing flows at all.

-- Robert A Cook, PE (Kennesaw, GA) (cook.r@csaatl.com), July 16, 1999.

Robert, you do have a way with the words.

-- Linda A. (adahi@muhlon.com), July 16, 1999.

Robert, Do you think it possible that Y2K glitches, which will spawn other secondary problems (i.e. Domino Effect) which spawn still more problems, will spread out exponentially through our technological societies to the point where it becomes impossible to stop. (possibly triggering an InfoMagic Scenario)?

I think most people are unaware of the explosive course exponential developments can take place.

-- Mark (quke@ix.netcom.com), July 16, 1999.

Thank you, Mr. Cook, for demonstrating as well the fallacy of using organic or "natural system" metaphors in evaluating man-made systems. A characteristic of natural systems is response to negative feedback, tending toward stability or steady-state.

Other than timely human intervention, I am nor aware of self-correcting mechanism inherent in man-made systems. Perhaps someone more educated in digital technology and systems theory would care to comment.

Hallyx

"Life is not a series of problems for which their are solutions, its a series of dilemmas for which there are trade-offs."

-- (Hallyx@aol.com), July 16, 1999.

Hallyx,

You don't need digital technology to see self correcting man made systems. They go back at least as far as the governor on a steam engine.

-- kozak (kozak@formerusaf.guv), July 17, 1999.

Right - that a mechanical limit - as is the pressure relief valves - required by law after nitwits and steamboat captains tried to "overpower" their primitive boilers to get more speed. Left uncontrolled by rules, most (many ?) people will take the easy way out - now, by not preparing - and "get by with the least amount of effort.

Again - the balance there (in the early 1890's) was "forced" by outside insurance groups and legistlation onto operators who were trying for gain "forced" the system too hard. Result? People were killed.

NOW - the opposite is occuring. To maintain political power by keeping the public "happy", and to satisfy their clients (the banks primarily) the current "rulers" - the only ones press listens to anyway (Clinton-Gore and their appointees) are doing the exact opposite.

The are covering up (worse - denying and ridiculing) the need for some level of preparations against uncertainity and loss of services. (This level of preparation - and we can disagree about what level is needed - would be what prevents panic and harm, and best premits easy recovery.) Result? Recovery will be greatly slowed, and the potential for panic made much worse.

Thus the "pressure" to cause problems is coming FROM the very people who should be at the heart of the effort to prevent problems. Instead of the FAA trying to protect the public - the FAA is trying to disguise the problem and deny that it is even now delaying airline arrivals through slow and improperly installed new equipment.

The original premis - that there could be a "very rapid" sudden dump of troubles - half the pond in one day - is not quite on target in that hte current situation is not quite true. A closer biological analogy is more the case is that there are millions of spores laying now out there dissolved in the water - under the right condition - unless they are removed from the system first - they will, in one night, all bloom at once and polute the water.

But now, you cannot see the polution - even with a microscope and focusing very closely, you can see only the spores. Later, you might be able to keep drinking the water, or you might not. We don't know yet. We do know that there is no otehr pond available.

-- Robert A Cook, PE (Kennesaw, GA) (cook.r@csaatl.com), July 17, 1999.

but MR. COOK SIR,the fish SEEM so FAT & HAPPY?

-- ponds-i love ponds. (dogs@zianet.com), July 18, 1999.

Sorry, Mr Kozak,

In my attempt at brevity (resulting from poor typing skills) I am sometimes misunderstood.

A mechanism designed to respond to or to provide feedback is a "design" function. ALL natural systems are constrained by some inherent feedback loop. Many man-made systems have feedback "designed" in; it is not a inherent characteristic.

Absent human intervention, should that mechanism fail, the system runs away, runs down or crashes. This is also true of some natural systems, by the way.

In Y2K terms, only human intervention can prevent our systems from crashing. Computers are not SELF-healing. The small question remains: Will we be capable of timely and sufficient intervention?

This would be a minor semantic point if the results of misunderstanding this were not so potentially serious.

Hallyx

"It is the mark of an educated mind to rest satisfied with the degree of precision which the nature of the subject admits and not to seek exactness where only an approximation is possible." -- Aristotle

Only if you consider a natural system as having been designed are feedback loops a design function.

-- (Hallyx@aol.com), July 18, 1999.