Zeno's paradoxes are a famous set of thought-provoking stories or puzzles created by Zeno of Elea in the mid-5th century BC. Philosophers, physicists, and mathematicians have argued for 25 centuries over how to answer the questions raised by Zeno's paradoxes.
Nine paradoxes have been attributed to him. Zeno constructed them to answer those who thought that Parmenides's idea that "all is one and unchanging" was absurd. Three of Zeno's paradoxes are the most famous: two are presented below. They all deal with problems of the apparently continuous nature of space and time.
In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres, for example. Suppose that each racer starts running at a constant speed, one very fast and one very slow. After some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the slower tortoise has run a much shorter distance. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther. It will then take still more time for Achilles to reach this third point, while the tortoise again moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.
Suppose someone wishes to get from point "A" to point "B". First, they must move halfway. Then, they must go half of the remaining way. Continuing in this manner, there will always be some small distance remaining, and the goal would never actually be reached. There will always be another number to add in a series such as 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... So, motion from any point "A" to any different point "B" seems an impossibility.
This then is where Zeno's paradox lies: both pictures of reality cannot be true at the same time. Hence, either:
1. There is something wrong with the way we perceive the continuous nature of time,
2. In reality there is no such thing as a discrete, or incremental, amounts of time, distance, or perhaps anything else for that matter, or
3. There is a third picture of reality that unifies the two pictures--the mathematical one and the common sense or philosophical one--that we do not yet have the tools to fully understand.
Few people would bet that the tortoise would win the race against an athlete. But, what is wrong with the argument?
As one begins adding the terms in the series 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ..., one may notice that the sum gets closer and closer to 1, and will never exceed 1. Aristotle (who is the source for much of what we know about Zeno) noted that as the distance (in the dichotomy paradox) decreases, the time to travel each distance gets exceedingly smaller and smaller. Before 212 BC, Archimedes had developed a method to get a finite answer for the sum of infinitely many terms which get progressively smaller (such as 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ...).
Modern calculus achieves the same result, using more rigorous methods.
Some mathematicians, such as Carl Boyer, think that Zeno's paradoxes are just mathematical problems, for which modern calculus provides a mathematical solution.
However, Zeno's questions remain problematic if one approaches an infinite series of steps, one step at a time. This is known as a 'supertask'. Calculus does not actually involve adding numbers one at a time. Instead, it determines the value (called a "limit" that the addition is approaching.
Mandrake
Mandrake is the common name of a number of plants in the Nightshade family, genus Mandragora. The roots often look like man or woman, or can be easily made to resemble them. The plant has been used in witchcraft for a long time.
According to this literature, the plant shrieks in pain, when it is pulled from the ground. This shriek is able to make a person deaf. He might also lose his mind, or even be killed, if he is unprotected.
Mandrake (Mandragora officinalis) has been used as an anaestethic for a long time. For this, it was usually prepared in an alcoholic solution.
Debian
Debian is a free operating system. It is a distribution of an operating system known as the GNU operating system, which can be used with various kernels, including Linux, kFreeBSD, and Hurd. In combination with these kernels, the operating system can be referred to as Debian GNU/Linux, Debian GNU/kFreeBSD, and Debian GNU/Hurd, respectively. Debian GNU/Linux is one of the most complete and popular GNU/Linux distributions, on which many others, like Ubuntu, are based.
The Debian Project officially started on August 16th, 1993, led by Ian Murdock. He was a computer programmer. Today, in this project, Debian is developed by more than 1,000 computer specialists all over the world.
The name "Debian" was taken after Ian Murdock and his wife Debra. Some people say or pronounce 'deb-ee-n' but others also say 'de-bi-an' or 'de-bai-an' and in Japan 'de-bi-a-n' and so on.
Software packages in development are either uploaded to the project distribution named "unstable" (also known as "sid"), or to the "experimental" repository. Software packages uploaded to "unstable" are normally versions stable enough to be released by the original upstream developer, but with the added Debian-specific packaging and other modifications introduced by Debian developers. These additions may be new and untested. Software not ready yet for the "unstable" distribution is typically placed in the "experimental" repository.
After a version of a software package has remained in "unstable" for a certain length of time (depending on how urgent the changes are), that package is automatically moved to the "testing" distribution. The package's move to testing happens only if no serious ("release-critical") bugs in the package are reported and if other software needed for package functionality qualifies for inclusion in "testing".
Since updates to Debian software packages between official releases do not contain new features, some choose to use the "testing" and "unstable" distributions for their newer packages. However, these distributions are less tested than "stable", and "unstable" does not receive timely security updates. In particular, incautious upgrades to working "unstable" packages can sometimes seriously break software functionality. Since September 9, 2005 the "testing" distributions security updates have been provided by the "testing" security team.
After the packages in "testing" have matured and the goals for the next release are met, the "testing" distribution becomes the next stable release. The latest stable release of Debian ("Buster") is 10.0, released on July 6, 2019. The next release is codenamed ""Bullseye"".
Due to an incident involving a CD vendor who made an unofficial and broken release labeled "1.0", an official 1.0 release was never made.
Debian has been ported to different architectures or platforms. One version, which is based on the developer release (sid) that has been ported to the Xbox is called Xebian.
Debian's official software package repository includes, for example, UNetbootin.
GNU
GNU is the name of a computer operating system. The name is short for "GNU's Not Unix". Richard Stallman leads the project working on GNU, known as the GNU Project. It was created to replace the UNIX operating system with all free and open source software. The popular Linux operating systems made using Linux kernel include a large number of GNU tools. Due to this reason, many projects and developers call the Linux based operating systems "GNU/Linux."