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My goal in teaching a martial arts class is that, when the students walk out the front door after class, they will be better prepared to defend themselves than when they walked in for class, this includes the very first class they attended. Intricate, complicated, and unnatural movements, exotic techniques, and weapons that are useless in modern society, may be a part of the art of a martial art (and Taekwondo has its share of them), but, they should not be confused with the martial part of a martial art. Taekwondo primarily uses hard block but when it comes to sparring, good fighters do not use hard or soft blocks, they evade or use the forearms in a tight guard to hopefully block attacks that were not avoided; hand and foot attacks are coming to fast to block. My chosen martial art is Taekwondo so I teach the art of Taekwondo, however, no matter its source, be it from Chinese Gung-fu or Icelandic Glima, if a martial technique floats, I teach it.
When I throw vertical punches into the water, they sink.
In Taekwondo, and most other martial arts, such as Shotokan, Shorin-ryu, and Goju-ryu, the fist rotates (twists) during a punch. However, a few martial arts styles, such as Isshin-ryu and some kung-fu styles, do not use the twist; their fist stays vertical during the punch and the thumb rests atop the fist rather than folding underneath.
Each camp has explanations as to why their method is stronger, faster, and better. My argument in punching is to look at natural movements and to look to those whose livelihood depends on the speed, power, and effectiveness of their punches—professional boxers. Boxers fold the thumb underneath and they twist their punches. It is a natural way to make a fist and a natural way to punch.
The following discusses horizontal and vertical punches and, since twisting or the lack of twisting is a part of the performing the punches, it is included in the discussion.
History of Punching
A simple punch was probably early man's first act of violence; it is instinctive. Irritate an infant and he or she will ball is or her fist and swat at you; it's what human's do. Punching is such a natural thing to humans, that apparently no one through the centuries thought it was special enough to merit mention, so their is little evidence of ancient punching techniques. As technology advanced, people were freed from having to work all day and night for their existence so they had more free time to think about more mundane things, such as why we punch the way we do.
Earliest evidence suggests that boxing was prevalent in North Africa during 4000 BC and the Mediterranean in 1500 BC. A Greek ruler named Thesus, who ruled around 900 B.C., was entertained by men who would seat in front of each other and beat another with their fists until one of them was killed. Over time, the fighters in the art of Pankration fought on their feet and wore gloves (not padded) and wrappings on their arms below the elbows, but were otherwise naked. Boxing was accepted as an Olympic sport (the ancient Greeks called it Pygmachia) in 688 B.C. Keeping their fingers free, fighters wore leather straps (called himantes) on their hands, wrists, and sometimes lower arms, to protect them from injury. For a guard, the fighters held the left arm held high and bent near the head, with the right arm free to hook and thrust. 
Image from a Panathenaic Amphora with scene of boxing match
336/335 B.C. British Museum
(Notice what appears to be vertical punches)
In Rome, fighters were usually criminals and slaves who hoped to become champions and gain their freedom. However, free men also fought and fist fighting became so popular that even aristocrats started fighting, but that was banned by the ruler Augustus. In 500 A.D., the sport was banned by Theodoric the Great.

Panathenaic Amphora with scene of boxing match
Early 5th c. BC. Athens, National Archaeological Museum, 1689
(Notice what appears to be vertical punches)
Records of boxing activity disappeared after the fall of the Roman Empire but it resurfaced in England during the early 18th century in the form of bare-knuckle prizefighting. The first documented account of a bare-knuckle fight in England appeared in 1681 in the "London Protestant Mercury," and the first English bare-knuckle champion was James Figg in 1719. This is also the time when the word "boxing" first came to be used.
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