# Law School Discussion

Nine Years of Discussion
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### AuthorTopic: The Biography of a Dangerous Idea  (Read 55099 times)

#### accumbens

• Newbie
• Posts: 3
##### Re: The Biography of a Dangerous Idea
« Reply #40 on: August 25, 2006, 08:40:38 PM »
A quantity that grows exponentially (or geometrically) is one whose growth rate is always proportional to its current size. Such growth is said to follow an exponential law. This implies that for any exponentially growing quantity, the larger the quantity gets, the faster it grows. But it also implies that the relationship between the size of the dependent variable and its rate of growth is governed by a strict law, of the simplest kind: direct proportion. It is proved in calculus that this law requires that the quantity is given by the exponential function, if we use the correct time scale. This explains the name.

Examples of exponential growth

Biology.
- Microorganisms in a culture dish will grow exponentially, at first, after the first microorganism appears (but then logistically until the available food is exhausted, when growth stops).
- 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 constant.
- 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 smooth (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.

Electrical engineering
- Charging and discharging of capacitors and changes in current in inductors are also exponential growth and decay phenomena. Engineers use a rule of five time constants to estimate when a steady state has been reached.

Computer technology
- Processing power of computers. See also Moore's law and technological singularity (under exponential growth, there are no such singularities).
- In computational complexity theory, computer algorithms of exponential complexity require an exponentially increasing amount of resources (e.g. time, computer memory) for only a constant increase in problem size. So for an algorithm of time complexity 2^x, if a problem of size x=10 requires 10 seconds to complete, then a problem of size x=11 will require 20 seconds, and x=12 will require 40 seconds. This kind of algorithm typically becomes unusable at very small problem sizes, often between 30 and 100 items (most computer algorithms need to be able to solve much larger problems, up to tens of thousands or even millions of items in reasonable times, something that would be physically impossible with an exponential algorithm). Also, the effects of Moore's Law do not help the situation much because doubling processor speed merely allows you to increase the problem size by one. E.g. if a slow processor can solve problems of size x in time t, then a processor twice as fast could only solve problems of size x+1 in the same time t. So exponentially complex algorithms are most often impractical, and the search for more efficient algorithms is one of the central goals of computer science.
- Internet traffic growth.

Investment. The effect of compound interest over many years has a substantial effect on savings and a person's ability to retire.

Physics
- Atmospheric pressure decreases exponentially with increasing height above sea level, at a rate of about 12% per 1000m.
- Nuclear chain reaction (the concept behind nuclear weapons). Each uranium nucleus that undergoes fission produces multiple neutrons, each of which can be absorbed by adjacent uranium atoms, causing them to fission in turn. If the probability of neutron absorption exceeds the probability of neutron escape (a function of the shape and mass of the uranium), k > 0 and so the production rate of neutrons and induced uranium fissions increases exponentially, in an uncontrolled reaction.
- Newton's law of cooling where T is temperature, t is time, and, A, D, and k > 0 are constants, is an example of exponential decay.

Multi-level marketing
- Exponential increases appear in each level of a starting member's downline as each subsequent member recruits more people.

#### libor

• Jr. Member
• Posts: 7
##### Re: The Biography of a Dangerous Idea
« Reply #41 on: August 25, 2006, 09:00:11 PM »

A quantity that grows exponentially (or geometrically) is one whose growth rate is always proportional to its current size. Such growth is said to follow an exponential law. This implies that for any exponentially growing quantity, the larger the quantity gets, the faster it grows. But it also implies that the relationship between the size of the dependent variable and its rate of growth is governed by a strict law, of the simplest kind: direct proportion. It is proved in calculus that this law requires that the quantity is given by the exponential function, if we use the correct time scale. This explains the name.

Another type of exponential growth is the Malthusian growth model. Sometimes called the simple exponential growth model, it is essentially exponential growth based on a constant rate of compound interest. Named after the Reverend Thomas Robert Malthus. At best, it can be described as an approximate physical law as it is generally acknowledged that nothing can grow at a constant rate indefinitely (Cassell's "Laws Of Nature," Professor James Trefil, 2002). Professor of Populations Joel E. Cohen has that the simplicity of the model makes it useful for very short-term predictions and of not much use for predictions beyond 10 or 20 years ("How Many People Can The Earth Support," 1995).

The Malthusian growth model is the direct ancestor of the logistic function. Pierre Francois Verhulst first published his logistic growth function in 1838 after he had read Malthus' "An Essay on the Principle of Population."

The sigmoid function

A logistic function or logistic curve models the S-curve of growth of some set P. The initial stage of growth is approximately exponential; then, as competition arises, the growth slows, and at maturity, growth stops. The untrammeled growth can be modelled as a rate term +rKP (a percentage of P). But then, as the population grows, some members of P (modelled as − rP2) interfere with each other in competition for some critical resource (which can be called the bottleneck, modelled by K). This competition diminishes the growth rate, until the set P ceases to grow (this is called maturity).

A logistic function is defined by the mathematical formula:

for real parameters a, m, n, and τ. These functions find applications in a range of fields, from biology to economics.

For example, in the development of an embryo, a fertilized ovum splits, and the cell count grows: 1, 2, 4, 8, 16, 32, 64, etc. This is exponential growth. But the fetus can grow only as large as the uterus can hold; thus other factors start slowing down the increase in the cell count, and the rate of growth slows (but the baby is still growing, of course). After a suitable time, the child is born and keeps growing. Ultimately, the cell count is stable; the person's height is constant; the growth has stopped, at maturity.

#### coordinated tie

• Jr. Member
• Posts: 8
##### Re: The Biography of a Dangerous Idea
« Reply #42 on: August 31, 2006, 09:50:04 PM »
Bell curve, S-curve, so many curves that I think I won't be able to remember their names ..
MY WAY OR

#### robmelone

• Full Member
• Posts: 92
##### Re: The Biography of a Dangerous Idea
« Reply #43 on: September 03, 2006, 10:40:03 PM »
It may well be the most potent force in the universe.

and the second most potent is. . .the might copy and paste!

Rob
http://www.cafepress.com/lawthug

#### Strong

• Sr. Citizen
• Posts: 398
##### Re: The Biography of a Dangerous Idea
« Reply #44 on: September 03, 2006, 11:13:59 PM »
In human-computer interaction, cut and paste or copy and paste is a user interface paradigm for transferring text, data, files or objects from a source to a destination. Most ubiquitous is the ability to cut and paste sections of plain text. This paradigm is closely associated with graphical user interfaces that use pointing devices.

The term cut and paste derives from the traditional practice in manuscript editing in which paragraphs were literally cut from a page with scissors and physically pasted onto another page. This was standard practice as late as the 1960s. Editing scissors with blades long enough to cut an 8-1/2"-wide page were available at stationery stores. The advent of photocopiers made the practice easier and more flexible.

The cut-and-paste paradigm was widely popularized by Apple in the Lisa (1981) and Macintosh (1984) operating systems and applications. It was mapped to a key combination consisting of a special control key held down while typing the letters X (for cut), C (for copy), and V (for paste). These key combinations were later adopted by Microsoft in Windows. Common User Access (in Windows and OS/2) also uses combinations of the Insert, Del, Shift and Control keys. Some environments allow cutting and pasting with a computer mouse (by drag and drop, for example).

#### or honor

• Newbie
• Posts: 4
##### Re: The Biography of a Dangerous Idea
« Reply #45 on: September 04, 2006, 07:58:03 PM »
Cut-'n-paste is king!
If someone could figure out a way to sell placebos for profit, they'd make a lot of money. Why, GNC already does it!

#### haystack

• Jr. Member
• Posts: 7
##### Re: The Biography of a Dangerous Idea
« Reply #46 on: September 04, 2006, 09:48:29 PM »
Quote
The cut-and-paste paradigm was widely popularized by Apple in the Lisa (1981) and Macintosh (1984) operating systems and applications. It was mapped to a key combination consisting of a special control key held down while typing the letters X (for cut), C (for copy), and V (for paste).

So basically the magical formula is X/V and C/V ?

#### morpheme

• Jr. Member
• Posts: 9
##### Re: The Biography of a Dangerous Idea
« Reply #47 on: September 12, 2006, 11:10:48 PM »
Keyboard commands are indeed important to know ... I'm pretty sure you will have to work one day with the keyboard commands alone ... a friend of mine had an instance when the screen froze completely and the mouse simply wouldn't work ... the only way to save a few files before actually shutting down the computer (and losing everything after a system restore was executed) was to use the functioning keyboard ...

#### bohr

• Newbie
• Posts: 3
##### Re: The Biography of a Dangerous Idea
« Reply #48 on: September 13, 2006, 06:17:57 AM »
morpheme!

#### cosė fan tutte

• Jr. Member
• Posts: 5
##### Re: Asia-Pacific Anger at North Korean missile launch
« Reply #49 on: September 24, 2006, 08:21:00 PM »

The Japanese Government has reacted angrily after a North Korean missile flew over its territory. Officials in Tokyo say the medium-range ballistic missile test-fired by North Korea on Monday landed in the Pacific Ocean, travelling much further than previously thought. Japanese Government officials said the missile was composed of two stages, the first of which landed in the Sea of Japan, with the second falling in waters off Japan's north-east coast. If confirmed, the test is the first reported launch by North Korea of a two-stage missile and marks a significant step forward in its rocket technology.

'Strong protest'

The Japanese Prime Minister Keizo Obuchi said on Monday his government had been aware of North Korea's preparations to launch a ballistic missile into the waters that divide the Korean peninsula from Japan. As a result, Japan has refused to sign an agreement on sharing the cost of providing safer nuclear reactors to North Korea and will protest to the North Koreans. Chief Cabinet Secretary Hiromu Nonaka expressed Japan's "strong protest" in a complaint to North Korea's representative at the United Nations. Tokyo and Pyongyang have no diplomatic relations. "It was an extremely dangerous act to conduct without any advance notice in the sea near Japan where a number of vessels and aircraft of our country are operating," Mr Nonaka said.

US concern

The United States expressed concern over the North Korean action. Correspondents say it is likely to overshadow talks which have resumed in New York between Washington and Pyongyang on the progress of an agreement by North Korea in 1994 to freeze its nuclear reprocessing programme.

North Korea's test programme

Russian officials have said the missile launch was a test which misfired. They announced the missile had landed inside their territorial waters and are reported to have sent warships to the area to investigate. South Korea's Defence Ministry identified the missile as a newly-developed Taepo-Dong One, with an estimated range of approximately 1,000 miles. In 1993, North Korea caused anxiety in Japan by test-firing a medium-range Rodong-1 missile into the Sea of Japan, demonstrating that parts of western Japan were within the 1,000km (600-mile) range of the missile. The BBC Tokyo correspondent says there is speculation that the latest missile firing was intended by North Korea as a show of power in advance of the 50th anniversary of the founding of the Stalinist state.

The U.S. isn't going to attack North Korea. It was going to attack Iraq as the exemplary action. In part, that's because Iraq's just a lot more important. It's right in the center of the oil-producing region, but in part it's because Iraq was understood to be completely defenseless. If you have any brains, you don't attack anybody who can defend itself. That's stupid. You want to attack somebody that's completely defenseless, and Iraq was known to be completely defenseless. That's why nobody was afraid of it, much as they might have hated it.

North Korea, on the other hand, has a deterrent. The deterrent is not nuclear weapons. It is conventional weapons -- massed artillery on the DMZ, the border with South Korea. Extensive massed artillery aimed at the capital, Seoul, South Korea, and at the U.S. troops in the south. Unless the Pentagon can figure out a way to get rid of that with precision weapons, or something or other, that is a deterrent to a U.S. attack. In fact, U.S. troops have since been withdrawn from the DMZ. And that's caused plenty of concern in both South and North Korea and the region, suggesting a very cynical strategy. You can figure it out. But what the U.S. was telling the world is if you don't want us to attack you and destroy you, you better have some kind of deterrent. And for most of the world, that's going to mean weapons of mass destruction. And terror.