How to mistress tangent effectively
There’s more to mastering the tangent than just being able to whip around a corner at high speed. Here are a few tips to help you master the art of the tangent.
1. Know your bike. Before you can master the tangent, you need to know your bike inside and out. Familiarize yourself with its weight and balance, and how it responds to your input.
2. Start slow. Don’t try to go full-throttle from the get-go. Accelerate gradually and increase your speed as you gain confidence.
3. Lean into the turn. As you approach a turn, lean your body weight into the turn. This will help your bike turn more smoothly and prevent you from losing control.
4. Use your legs. When leaning into a turn, use your legs to help stabilize your bike. Put your inside leg up on the peg and press down with your outside leg.
5. Look where you want to go. As with anything, where you look is where you’ll end up. So, when taking a turn, look through the turn to where you want to exit. This will help your body and bike follow suit.
6. Practice, practice, practice. The more you practice, the better you’ll get at negotiating turns. Find a safe place to practice, such as an empty parking lot, and get comfortable with your bike.
With these tips in mind, go out and master the tangent!.Extra resources
Origins of mistress tangent
A mistress tangent is a math problem in which the answer seems to approach a certain value, but then abruptly changes direction and heads towards infinity. The term was coined by mathematician Stan Wagon in 1992, in reference to a particular type of curve that behaves in this way.
The most famous example of a mistress tangent is the so-called “false position” method of solving equations, which was popularized by the 17th century mathematician Isaac Newton. In this method, one assumes that the roots of an equation lie between two known values, and then uses the equation to find a new estimate for one of those values. However, if the initial estimate is not close enough to the true root, the new estimate will be even further away, leading to ever-increasing error. As Wagon puts it, “each successive approximation is a little bit worse than the one before.”
The false position method is just one example of a more general phenomenon, known as “divergence.” Divergence occurs whenever a process generates a sequence of values that gets further and further away from some desired value. In the case of the false position method, the desired value is the root of the equation, but divergence can occur in other contexts as well. For instance, a sequence of numbers may diverge to infinity if it is generated by a process that is “zooming in” on a point that does not actually exist.
One of the most famous examples of divergence is the so-called “halting problem,” first proposed by the mathematician Alan Turing in 1936. The halting problem is, essentially, the problem of trying to write a program that can tell whether or not any other given program will eventually come to a halt. Turing showed that this is impossible, in the sense that there is no program that can do it for all possible programs.
The proof of the halting problem is closely related to the phenomenon of mistress tangents. In essence, it shows that any attempt to write a program that can solve the halting problem will inevitably lead to a mistress tangent-like situation, in which the program gets further and further away from the desired answer.
The connections between the halting problem and mistress tangents have been explored in detail by the mathematician Christopher Langton, who has proposed a general theory of “computational irreducibility.” This theory is closely related to the work of Stephen Wolfram on “cellular automata,” and it has implications for everything from the origins of life to the behavior of stock markets.
At its heart, the theory of computational irreducibility says that some problems are simply too difficult to solve, even with the aid of a computer. This may seem like a depressing conclusion, but it also has a certain kind of beauty. In a sense, it says that the universe is ultimately mystery, and that we should never expect to fully understand it.
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