Parable of the Invisible Gardener

The Parable of the Invisible Gardener is a tale told by John Wisdom. It was later developed in the university debate, by Antony Flew who made a few changes such as changing the gardeners to explorers. It is often used to illustrate the perceived differences between assertions based on faith and assertions based on scientific evidence, and the problems associated with unfalsifiable beliefs. The main point of the parable is that religious believers do not allow anybody to "falsify" their assertions, instead they simply change their beliefs to suit the questioner. This is why for Flew religious believers cause God to "Die the death of a thousand qualifications". The tale runs as follows:

"Two people return to their long neglected garden and find, among the weeds, that a few of the old plants are surprisingly vigorous. One says to the other, 'It must be that a gardener has been coming and doing something about these weeds.' The other disagrees and an argument ensues. They pitch their tents and set a watch. No gardener is ever seen. The believer wonders if there is an invisible gardener, so they patrol with bloodhounds but the bloodhounds never give a cry. Yet the believer remains unconvinced, and insists that the gardener is invisible, has no scent and gives no sound. The skeptic doesn't agree, and asks how a so-called invisible, intangible, elusive gardener differs from an imaginary gardener, or even no gardener at all."

In the later additions of Flew, there is the addition of infra-red, and cameras and the garden/clearing is surrounded by an electrified fence. The gardener therefore must not only be undetectable, but intangible.

British philosopher of religion Antony Flew (1923-2010), writing as an atheist in 1955, expanded upon a parable designed to show that there is no difference between (God as) an “invisible gardener” and there being “no gardener at all.”

Once upon a time two explorers came upon a clearing in the jungle. In the clearing were growing many flowers and many weeds.

One explorer says, “Some gardener must tend this plot.”

The other disagrees, “There is no gardener.”

So they pitch their tents and set a watch.

No gardener is ever seen.

“But perhaps he is an invisible gardener.”

So they set up a barbed-wire fence. They electrify it. They patrol with bloodhounds. (For they remember how H. G. Well’s The Invisible Man could be both smelt and touched though he could not be seen.)

But no shrieks ever suggest that some intruder has received a shock. No movements of the wire ever betray an invisible climber. The bloodhounds never give cry.

Yet still the Believer is not convinced. “But there is a gardener, invisible, intangible, insensible, to electric shocks, a gardener who has no scent and makes no sound, a gardener who comes secretly to look after the garden which he loves.”

At last the Skeptic despairs, “But what remains of your original assertion? Just how does what you call an invisible, intangible, eternally elusive gardener differ from an imaginary gardener or even from no gardener at all?”

John Frame counters with a parable of his own:

Once upon a time two explorers came upon a clearing in the jungle.

A man was there, pulling weeds, applying fertilizer, trimming branches. The man turned to the explorers and introduced himself as the royal gardener. One explorer shook his hand and exchanged pleasantries.

The other ignored the gardener and turned away: “There can be no gardener in this part of the jungle,” he said; “this must be some trick.”

They pitch camp. Every day the gardener arrives, tends the plot. Soon the plot is bursting with perfectly arranged blooms.

“He’s only doing it because we’re here—to fool us into thinking this is a royal garden.”

The gardener takes them to a royal palace, introduces the explorers to a score of officials who verify the gardener’s status.

Then the skeptic tries a last resort: “Our senses are deceiving us. There is no gardener, no blooms, no palace, no officials. It’s still a hoax!”

Finally the believer despairs: “But what remains of your original assertion? Just how does this mirage, as you call it, differ from a real gardener?”

—John M. Frame, “God and Biblical Language: Transcendence and Immanence,” God’s Inerrant Word, ed. J. W. Montgomery (Minneapolis: Bethany Fellowship, 1974), p. 171.

Butterfly effect

From Wikipedia, the free encyclopedia

For other uses, see Butterfly effect (disambiguation).

Point attractors in 2D phase space

In chaos theory, the butterfly effect is the sensitive dependency on initial conditions in which a small change at one place in a deterministic nonlinear system can result in large differences in a later state. The name of the effect, coined by Edward Lorenz, is derived from the theoretical example of the details of a hurricane (exact time of formation, exact path taken) being influenced by minor perturbations equating to the flapping of the wings of a distant butterfly several weeks earlier. Lorenz discovered the effect when he observed that runs of his weather model with initial condition data that wasrounded in a seemingly inconsequential manner would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.

Although the butterfly effect may appear to be an unlikely behavior, it is exhibited by very simple systems. For example, a ball placed at the crest of a hill may roll into any surrounding valley depending on, among other things, slight differences in its initial position. Also the randomness of throwing adice depends on this system's characteristic to amplify small differences in initial conditions - the throw - into significantly different dice paths and outcome, which makes it virtually impossible to throw a dice exactly the same way twice.

The butterfly effect is a common trope in fiction, especially in scenarios involving time travel. Additionally, works of fiction that involve points at which the storyline diverges during a seemingly minor event, resulting in a significantly different outcome than would have occurred without the divergence, are an example of the butterfly effect.

Chaos theory and the sensitive dependence on initial conditions was described in the literature in a particular case of the three-body problem by Henri Poincaré in 1890.^[1] He later proposed that such phenomena could be common, for example, in meteorology.^[2]

In 1898,^[1] Jacques Hadamard noted general divergence of trajectories in spaces of negative curvature. Pierre Duhem discussed the possible general significance of this in 1908.^[1] The idea that one butterflycould eventually have a far-reaching ripple effect on subsequent historic events first appears in "A Sound of Thunder", a 1952 short story by Ray Bradbury about time travel (see Literature and print here).

In 1961, Lorenz was using a numerical computer model to rerun a weather prediction, when, as a shortcut on a number in the sequence, he entered the decimal 0.506 instead of entering the full 0.506127. The result was a completely different weather scenario.^[3] In 1963 Lorenz published a theoretical study of this effect in a well-known paper called Deterministic Nonperiodic Flow.^[4] (As noted in the paper, the calculations were performed on a Royal McBee LPD-30 computing machine.^[5]) Elsewhere he said^{[citation needed]} that "One meteorologist remarked that if the theory were correct, one flap of a seagull's wings could change the course of weather forever." Following suggestions from colleagues, in later speeches and papers Lorenz used the more poetic butterfly. According to Lorenz, when he failed to provide a title for a talk he was to present at the 139th meeting of the American Association for the Advancement of Science in 1972, Philip Merilees concocted Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? as a title. Although a butterfly flapping its wings has remained constant in the expression of this concept, the location of the butterfly, the consequences, and the location of the consequences have varied widely.^[6]

The phrase refers to the idea that a butterfly's wings might create tiny changes in the atmosphere that may ultimately alter the path of a tornado or delay, accelerate or even prevent the occurrence of a tornado in another location. Note that the butterfly does not power or directly create the tornado. The Butterfly effect does not convey the notion - as is often misconstrued - that the flap of the butterfly's wingscauses the tornado. The flap of the wings is a part of the initial conditions; one set of conditions leads to a tornado while the other set of conditions doesn't. The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale alterations of events (compare: domino effect). Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different - it's possible that the set of conditions without the butterfly flapping its wings is the set that leads to a tornado.

The butterfly effect presents an obvious challenge to prediction, since initial conditions for a system such as the weather can never be known to complete accuracy. This problem motivated the development of ensemble forecasting, in which a number of forecasts are made from perturbed initial conditions.^[7]

Some scientists have since argued that the weather system is not as sensitive to initial condition as previously believed.^[8] David Orrell argues that the major contributor to weather forecast error is model error, with sensitivity to initial conditions playing a relatively small role.^[9][10] Stephen Wolfram also notes that the Lorenz equations are highly simplified and do not contain terms that represent viscous effects; he believes that these terms would tend to damp out small perturbations.^[11]

Illustration[edit]

The butterfly effect in the Lorenz attractor
time 0 ≤ t ≤ 30 (larger)		z coordinate (larger)
These figures show two segments of the three-dimensional evolution of two trajectories (one in blue, the other in yellow) for the same period of time in the Lorenz attractor starting at two initial points that differ by only 10−5 in the x-coordinate. Initially, the two trajectories seem coincident, as indicated by the small difference between the z coordinate of the blue and yellow trajectories, but for t > 23 the difference is as large as the value of the trajectory. The final position of the cones indicates that the two trajectories are no longer coincident at t = 30.
A Java animation of the Lorenz attractor shows the continuous evolution.

Theory and mathematical definition[edit]

Recurrence, the approximate return of a system towards its initial conditions, together with sensitive dependence on initial conditions, are the two main ingredients for chaotic motion. They have the practical consequence of making complex systems, such as the weather, difficult to predict past a certain time range (approximately a week in the case of weather) since it is impossible to measure the starting atmospheric conditions completely accurately.

A dynamical system displays sensitive dependence on initial conditions if points arbitrarily close together separate over time at an exponential rate. The definition is not topological, but essentially metrical.

If M is the state space for the map , then  displays sensitive dependence to initial conditions if for any x in M and any δ > 0, there are y in M, with  such that

The definition does not require that all points from a neighborhood separate from the base point x, but it requires one positive Lyapunov exponent.

Examples[edit]

The butterfly effect is most familiar in terms of weather; it can easily be demonstrated in standard weather prediction models, for example.^[12]

The potential for sensitive dependence on initial conditions (the butterfly effect) has been studied in a number of cases in semiclassical and quantum physics including atoms in strong fields and the anisotropic Kepler problem.^[13][14] Some authors have argued that extreme (exponential) dependence on initial conditions is not expected in pure quantum treatments;^[15][16] however, the sensitive dependence on initial conditions demonstrated in classical motion is included in the semiclassical treatments developed by Martin Gutzwiller^[17] and Delos and co-workers.^[18]

Other authors suggest that the butterfly effect can be observed in quantum systems. Karkuszewski et al. consider the time evolution of quantum systems which have slightly different Hamiltonians. They investigate the level of sensitivity of quantum systems to small changes in their given Hamiltonians.^[19] Poulin et al. presented a quantum algorithm to measure fidelity decay, which "measures the rate at which identical initial states diverge when subjected to slightly different dynamics". They consider fidelity decay to be "the closest quantum analog to the (purely classical) butterfly effect".^[20] Whereas the classical butterfly effect considers the effect of a small change in the position and/or velocity of an object in a given Hamiltonian system, the quantum butterfly effect considers the effect of a small change in the Hamiltonian system with a given initial position and velocity.^[21][22] This quantum butterfly effect has been demonstrated experimentally.^[23] Quantum and semiclassical treatments of system sensitivity to initial conditions are known as quantum chaos.^[15][21]

how does bee know hexagon?

How does the Bee know the shape of Hexagon? Where did they learn from?

Honeycomb is one of the most amazing structures. The structure is a result of an amazing effort by which the volume and precision of containing the honey is most optimistic.

Take a look at the following diagrams....

Honeybees are some of nature's finest mathematicians. Not only can they calculate angles and comprehend the roundness of the earth, these smart insects build and live in one of the most mathematically efficient architectural designs around: the beehive. Zack Patterson and Andy Peterson delve into the very smart geometry behind the honeybee's home. 

Straw that broke the camel's back

The idiom the straw that broke the camel's back is from an Arabic proverb about how a camel is loaded beyond its capacity to move or stand.^[1] This is a reference to any process by which cataclysmic failure (a broken back) is achieved by a seemingly inconsequential addition, a single straw. This also gives rise to thephrase "the last/final straw", used when something is deemed to be the last in a line of unacceptable occurrences. Variations include "the straw that broke thedonkey's back", the "melon that broke the monkey's back", the "feather that broke the camel's back", and the "straw that broke the horse's back".

One of the earliest published usages of this phrase was in Charles Dickens's Dombey and Son (1848), where he says "As the last straw breaks the laden camel's back", meaning that there is a limit to everyone's endurance, or everyone has his breaking-point. Dickens was writing in the nineteenth century and he may have received his inspiration from an earlier proverb, recorded by Thomas Fuller in hisGnomologia: Adages and Proverbs as "'Tis the last feather that breaks the horse's back". Mark Twain also used a variation of this phrase in his book The Adventures of Tom Sawyer (1876), "this final feather broke the camel's back" 

Camel's nose

The camel's nose is a metaphor for a situation where the permitting of a small, seemingly innocuous act will open the door for larger, clearly undesirable actions.

A typical usage is this, from U.S. Senator Barry Goldwater in 1958:

This bill and the foregoing remarks of the majority remind me of an old Arabian proverb: "If the camel once gets his nose in the tent, his body will soon follow." If adopted, the legislation will mark the inception of aid, supervision, and ultimately control of education in this country by the federal authorities.^[1]

According to Geoffrey Nunberg, the image entered the English language in the middle of the 19th century.^[2] An early example is a fable printed in 1858 in which an Arab miller allows a camel to stick its nose into his bedroom, then other parts of its body, until the camel is entirely inside and refuses to leave.^[3] Lydia Sigourney wrote another version, a widely reprinted poem for children, in which the camel enters a shop because the workman does not forbid it at any stage.^[4]

The 1858 example above says, "The Arabs repeat a fable", and Sigourney says in a footnote, "To illustrate the danger of the first approach of evil habit, the Arabs have a proverb, 'Beware of the camel's nose.'" However, Nunberg could not find an Arab source for the saying and suspected it was a Victorian invention.^[2]

An early citation with a tent is "The camel in the Arabian tale begged and received permission to insert his nose into the desert tent."^[5] By 1878, the expression was familiar enough that part of the story could be left unstated. "It is the humble petition of the camel, who only asks that he may put his nose into the traveler's tent. It is so pitiful, so modest, that we must needs relent and grant it."^[6]

In a 1915 book of fables by Horace Scudder, the story, titled The Arab and His Camel, ends with the moral: "It is a wise rule to resist the beginnings of evil."^[7]

The phrase was used in Reed v. King (193 CA Rptr. 130 - 1983): "The paramount argument against an affirmative conclusion is it permits the camel's nose of unrestrained irrationality admission to the tent. If such an 'irrational' consideration is permitted as a basis of rescission the stability of all conveyances will be seriously undermined." The case in question involved a plaintiff suing because the defendant sold a house without telling them that the house's previous inhabitants had been brutally murdered 10 years earlier.

There are a number of other metaphors and expressions which refer to small changes leading to chains of events with undesirable or unexpected consequences, differing in nuances.

The usage:

The Bible says: Ephesians 4:27 NIV

and do not give the devil a foothold.

God knows that giving a slightest of detail to devil will take control of the whole person. 

Matthew 12:43-45

New King James Version (NKJV)

An Unclean Spirit Returns

43 “When an unclean spirit goes out of a man, he goes through dry places, seeking rest, and finds none. 44 Then he says, ‘I will return to my house from which I came.’ And when he comes, he finds it empty, swept, and put in order. 45 Then he goes and takes with him seven other spirits more wicked than himself, and they enter and dwell there; and the last state of that man is worse than the first. So shall it also be with this wicked generation.”

Time Management

Time Management

A professor stood before his philosophy class and had some items in front of him. When the class began, wordlessly, he picked up a very large and empty mayonnaise jar and proceeded to fill it with golf balls. He then asked the students if the jar was full. They agreed that it was.

So the professor then picked up a box of pebbles and poured them into the jar. He shook the jar lightly. The pebbles rolled into the open areas between the golf balls. He then asked the students again if the jar was full. They agreed it was.

The professor next picked up a box of sand and poured it into the jar. Of course, the sand filled up everything else. He asked once more if the jar was full. The students responded with an unanimous “yes.”

The professor then produced two cups of coffee from under the table and poured the entire contents into the jar, effectively filing the space between the grains of sand.

The professor then started talking to the students. “My dear students, the jar is now full, but what is the message.” One student stood raised his hand and said, “However busy we might be, there is always time for some more work.” Good, said the professor, but I would like to add some more.

The students look curiously at the professor as he continued. However busy we may be, we can always find time for more work is right, but what if the sequence in which the items were placed in the jar was reversed.

Would there still be enough space for all things to be placed in the jar. So, my friends, the important thing in life is to understand your priorities. What things must go in first and which ones later. Once you have it right, it will all fit in well.

10/12/10

The Glad Game... Pollyanna principle

The Pollyanna principle (also called Pollyannaism or positivity bias) is the tendency for people to remember pleasant items more accurately than unpleasant ones. Research indicates that, at the subconscious level, the mind has a tendency to focus on the optimistic while, at the conscious level, it has a tendency to focus on the negative. This subconscious bias towards the positive is often described as the Pollyanna principle.

The name derives from the 1913 novel Pollyanna by Eleanor H. Porter describing a girl who plays the "glad game"—trying to find something to be glad about in every situation. The novel has been adapted to film several times, most famously in 1920 and 1960. An early use of the name "Pollyanna" in psychological literature was in 1969 by Boucher and Osgood who described a Pollyanna hypothesis as a universal human tendency to use evaluatively positive words more frequently and diversly than evaluatively negative words in communicating.
The Pollyanna principle was described by Matlin and Stang in 1978 using the archetype of Pollyanna more specifically as a psychological principle which portrays the positive bias people have when thinking of the past. According to the Pollyanna Principle, the brain processes information that is pleasing and agreeable in a more precise and exact manner as compared to unpleasant information. We actually tend to remember past experiences as more rosy than they actually occurred.
The researchers Margaret Matlin and David Stang provided substantial evidence of the Pollyanna Principle. They found that people expose themselves to positive stimuli and avoid negative stimuli, they take longer to recognize what is unpleasant or threatening than what is pleasant and safe, and they report that they encounter positive stimuli more frequently than they actually do. Matlin and Stang also determined that selective recall was a more likely occurrence when recall was delayed: the longer the delay, the more selective recall that occurred.
However, the Pollyanna principle does not apply to individuals suffering from depression or anxiety, who tend to either have more depressive realism or a negative bias.

Ways to look at Failure...

Thomas Edison tried and failed nearly 2,000 times to develop the carbonized cotton-thread filament for the incandescent light bulb.

And when asked about it, he said "I didn't fail; I found out 2,000 ways how not to make a light bulb," but he only needed one way to make it work.

Looking for Dirt or Gold?

Andrew Carnegie, America's first great industrialist, nearly 100 years ago had 43 millionaires working for him - an unheard-of occurrence in those days.  A reporter asked him how he managed to hire 43 millionaires.  Carnegie responded that none of them were millionaires when he hired them but observed that, "You develop millionaires the way you mine gold.  You expect to move tons of dirt to find an ounce of gold, but you don't go into the mine looking for the dirt—you go in looking for the gold."

Motivating People - From the Book "The Leader In You"

Even as a boy Andrew Carnegie discovered the astonishing importance that people place on their names. When he was ten years old, he had a father rabbit and a mother rabbit. He awoke one morning to discover that he had a whole next full of little rabbits and nothing to feed them.
What do you suppose he did? Well, he had a brilliant idea. He told half a dozen boys in the neighborhood that if they would go out everyday and pull enough dandelions and grass and clover to feed the rabbits, he would name the rabbits in their honor. The plan worked like magic, and here is the point of the story.
Andrew Carnegie never forgot that incident. And years later, he made millions of dollars by using the same technique in business. He wanted to sell steel rails to the Pennsylvania Railroad. J. Edgar Thomson was president of the railroad then. So Andrew Carnegie, remembering the lesson he had learned from his rabbits, built a huge steel mill in Pittsburgh and called it the J. Edgar Thomson Steel works.
Now let me ask you a question. When the Pennsylvania Railroad needed steel rails after that, where do you suppose J. Edgar Thomson bought them?
                                                                -- Dale Carnegie

Carz Vs Computers

At a computer expo (COMDEX), Bill Gates reportedly compared the computer industry with the auto industry and stated: "If GM had kept up with the technology like the computer industry has, we would all be driving $25.00 cars that got 1,000 miles to the gallon." 

In response to Bill's comments, General Motors issued a press release (by Mr. Welch himself) stating: 
 

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If GM had developed technology like Microsoft, we would all be driving cars with the following characteristics: 

1. For no reason at all, your car would crash twice a day. 

2. Every time they repainted the lines on the road, you would have to buy a new car. 

3. Occasionally, executing a manoeuver such as a left-turn would cause your car to shut down and refuse to restart, and you would have to reinstall the engine. 

4. When your car died on the freeway for no reason, you would just accept this, restart and drive on. 

5. Only one person at a time could use the car, unless you bought 'Car95' or 'CarNT', and then added more seats. 

6. Apple would make a car powered by the sun, reliable, five times as fast, and twice as easy to drive, but would run on only five per cent of the roads. 

7. Oil, water temperature and alternator warning lights would be replaced by a single 'general car default' warning light. 

8. New seats would force every-one to have the same size butt. 

9. The airbag would say 'Are you sure?' before going off. 

10. Occasionally, for no reason, your car would lock you out and refuse to let you in until you simultaneously lifted the door handle, turned the key, and grabbed the radio antenna. 

11. GM would require all car buyers to also purchase a deluxe set of road maps from Rand-McNally (a subsidiary of GM), even though they neither need them nor want them. Trying to delete this option would immediately cause the car's performance to diminish by 50 per cent or more. Moreover, GM would become a target for investigation by the Justice Department. 

12. Every time GM introduced a new model, car buyers would have to learn how to drive all over again because none of the controls would operate in the same manner as the old car. 

13. You would press the 'start' button to shut off the engine.
Read more at http://www.snopes.com/humor/jokes/autos.asp#eKie7TGxsFr0jDfg.99

“The Christian says, 'Creatures are not born with desires unless satisfaction for those desires exists. A baby feels hunger: well, there is such a thing as food. A duckling wants to swim: well, there is such a thing as water. Men feel sexual desire: well, there is such a thing as sex. If I find in myself a desire which no experience in this world can satisfy, the most probable explanation is that I was made for another world. If none of my earthly pleasures satisfy it, that does not prove that the universe is a fraud. Probably earthly pleasures were never meant to satisfy it, but only to arouse it, to suggest the real thing. If that is so, I must take care, on the one hand, never to despise, or to be unthankful for, these earthly blessings, and on the other, never to mistake them for the something else of which they are only a kind of copy, or echo, or mirage. I must keep alive in myself the desire for my true country, which I shall not find till after death; I must never let it get snowed under or turned aside; I must make it the main object of life to press on to that country and to help others to do the same.”

― C.S. Lewis, Mere Christianity

contemplative mood

“It (the notion of gravity) was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the Earth's centre?”

“Therefore does this apple fall perpendicularly or towards the centre? If matter thus draws matter; it must be proportion of its quantity. Therefore the apple draws the Earth, as well as the Earth draws the apple."

The Big Rocks Of Life

Dr. Stephen R. Covey,
First Things First

---

One day this expert was speaking to a group of business students and, to drive home a point, used an illustration I’m sure those students will never forget. After I share it with you, you’ll never forget it either.

As this man stood in front of the group of high-powered over-achievers he said, "Okay, time for a quiz." Then he pulled out a one-gallon, wide-mouthed mason jar and set it on a table in front of him. Then he produced about a dozen fist-sized rocks and carefully placed them, one at a time, into the jar.
When the jar was filled to the top and no more rocks would fit inside, he asked, "Is this jar full?" Everyone in the class said, "Yes." Then he said, "Really?" He reached under the table and pulled out a bucket of gravel. Then he dumped some gravel in and shook the jar causing pieces of gravel to work themselves down into the spaces between the big rocks.
Then he smiled and asked the group once more, "Is the jar full?" By this time the class was onto him. "Probably not," one of them answered. "Good!" he replied. And he reached under the table and brought out a bucket of sand. He started dumping the sand in and it went into all the spaces left between the rocks and the gravel. Once more he asked the question, "Is this jar full?"
"No!" the class shouted. Once again he said, "Good!" Then he grabbed a pitcher of water and began to pour it in until the jar was filled to the brim. Then he looked up at the class and asked, "What is the point of this illustration?"
One eager beaver raised his hand and said, "The point is, no matter how full your schedule is, if you try really hard, you can always fit some more things into it!"
"No," the speaker replied, "that’s not the point. The truth this illustration teaches us is: If you don’t put the big rocks in first, you’ll never get them in at all."

What are the big rocks in your life? A project that you want to accomplish? Time with your loved ones? Your faith, your education, your finances? A cause? Teaching or mentoring others? Remember to put these Big Rocks in first or you’ll never get them in at all.