Mostly, tapering works because of rest. Now, if you’re on a track and field team, and practice ends early, you’re probably tapering. The reason it works is because it helps you get more rest and allows you to burn less calories, so when the day comes, you have a lot of energy for your 5K or half-marathon, or 4K. It works with swimming, too. As your muscles work out less, you are less likely to be sore after practice, allowing you to have a lot of energy at districts or states, or whatever.

Tapering also works in academic situations with your brain, too. If you’re taking some sort of standardized test, you’re still expected to do classwork, right? So how are we supposed to taper with our brains. The answer is usually in homework. Teachers often don’t assign homework when students have to take standardized tests. But what if you’re taking the SAT’s, where teachers will still give you homework? Tapering works as if you’re working your brain less. People don’t study as much towards the test and look to gain more sleep. They also never do last-minute studying. That way, like most tapering, you have energy for the test, and that energy can be used for ultra brainpower.

Whether it’s the SAT’s, a marathon, or a district race you’re preparing for, you need to taper. Tapering helps ease your muscles or brain so the next day, your energy levels are high. The energy converts into muscle or brainpower. Hopefully you win, whether on the test, in the pool, or on the tracks!

]]>First, water has big benefits over sports drinks. First, they have no sugar. This is a huge advantage already because of no sugar, so you can’t have a sugar crash or gaining instead of burning calories. The only disadvantage it as is that there are no special effects to the water, like electrolytes or other particles. Fortunately, there are some waters out there that do have electrolytes built in to the water, like Smart Water, that have things like electrolytes.

Next, sports drinks also have big benefits over water, too, like they are especially made for athletes that train hard. They replenish electrolytes and give you an extra sugar boost. However, the sugar may have its disadvantages. Since sports drinks have large amounts of sugar, you might gain weight rather than lose weight if that’s the effect you want.

Now, which drink is better. In my opinion, water should be drank by athletes who only exercise for 30 minutes a day, and mild workouts. Sports drinks should only be drank if the workouts you are doing are very rigorous or physically demanding. If not, then just stick to your tap water.

]]>That decides where we go?

Is it the road we take

Is it the road we don’t take

Or is it both?

Is time already decided

For us or not?

Whether Schrodinger thinks we do or not

Or whether the cat is alive or dead

Does it matter at all in our lives?

What is the matter whether

I take both tracks

Yet I will only choose one?

All I know

Is that thinking is the way

That came up with it all,

Whether both paths or one.

]]>David Hilbert was a German mathematician. Near his age of the early 20th century, there was a need for discovering the foundations of math, since there were paradoxes and inconsistencies, like 1/0. So, Hilbert tried to create a program so they could strip arithmetic to the minimum. He would try to make all things in arithmetic without any misconceptions, so they could solve some questions they never could have with other method. But it failed. David Hilbert would find the truth off of Kurt Gödel.

Kurt Gödel was also a German mathematician that also wanted to discover the bare bones of arithmetic. However, looking at Hilbert’s Program, he realized that the attempts were fruitless and published his incompleteness theorems. It states that we cannot discover everything about arithmetic through equations and formulas. It shook the world as we knew it, with the most shaking theorem ever written.

Even though we would love to find the true basis of arithmetic, along with David Hilbert, Kurt Gödel proved they would be fruitless. This theorem proved that some problems were unsolvable. It might have saddened some people, but it is a great discovery as a theory to attack unprovable theories.

]]>A concept is really important to prove this theory. First, there are infinitely many numbers between any number. Say you say 1/2. Well, there’s 0.51 and 0.501. Or there’s 0.50000000001. You get what I mean. But 0.999… doesn’t follow these rules. There are no decimals bigger than 0.999… but less than 1. This shows that 0.999… isn’t like the other numbers.If there isn’t a number between them, then 0.999… = 1.

There are other various proofs that 0.999… = 1. Like how 1/3 is 0.333…. and if you multiply 1/3 by 3 you get 0.999… or 3/3 or 1. There are other internet proofs out there that prove that 0.999… = 1. But mainly the reason is that it works. It doesn’t fail at any job. It can operate fine even with this.

So maybe there’s a proof out there that says no, but I have the evidence to say that 0.999… = 1. Through rules of numbers and fractions, 0.999… = 1, whether you think no or yes. But yeah, whether there’s a little something between 0.999… and 1 is debatable, which is why this question will be asked over and over again.

]]>A really powerful sense of ours is the eye. Although it does help us see, understanding it is important to describe where all colors come from. White is light, and black is the absence of light. But how do we know that other colors, like pink, green, blue, and red exist.? The light is what really helps perceive different colors.

This prism is the reason why we see colors. The rainbow that reflects off is the example of all of the colors that are possible. This way, we know that colors are real.

Now differentiation between colors is through the light we see. If the shape you’re looking at is blue, the blue light shines into your eyes and now your brain knows it as blue. Same goes with all other colors. Some animals, though, cannot perceive some colors. Dogs cannot see red.Our man eye is one of the best at perceiving colors. But when you are colorblind, sometimes the difference between red and green is nothing.

Colors revolutionize what we see and helps us make choices in life. Our eyes are responsible for this great sight vision, and even though us humans may not be the smartest species out there, it seems like we can’t see the future coming ahead. If a species can see that, I will be surprised.

]]>First, we must talk about a fundamental theorem in trigonometry: the Pythagorean theorem. This states that the two shorter sides on a right triangle are squared and added, will the longer side, or the hypotenuse, squared. This principle brought trigonometry to life, and soon, more things were being discovered about right triangles, and soon people realized how effective they were.

There are three main trigonometric ratios that you need to know. The first is sine. If you take a sine of an angle of a certain amount of degrees, it will show you how big the opposite side is compared to the hypotenuse. Next is cosine. Similar to sine, if you take cosine of x degrees, it will show you how big the side that makes the angle (and s not the hypotenuse) compared to the hypotenuse. Finally, is tangent. If you take a tangent to a certain amount of degrees, it will show you how big the opposite side is compared to the adjacent side (either of them are not the hypotenuse).

Trigonometry was really the base of western mathematics and trigonometry is a real world concept that can help finding side lengths using angles and other things.There are a lot more topics in trigonometry, but if you are interested, study trigonometry. It can teach you a lot of stuff that is useful in different careers.

]]>The intelligence that most people really think about when they talk about intelligence and smarts are if they know something or they don’t. It makes sense because the smartest people have good grades and they get good grades because they know stuff. Right? The only thing is that some people are smart, not naturally, but from experience and that lightbulb after 23 years of age. Adding, if there was a definition of smart, then there should be a line saying what you need to be smart. There is no such thing. We need a definition that can fit the requirements well.

Maybe we have been thinking that intelligence is all about what you know when really, it should be how you learn it in the first place. This definition of smart is to be a quick learner. This kind of makes sense because being a quick learner means you can learn things quickly, which in turn allows you to process more information, and let you know more. This describes more because it helps make a bigger conclusion in the end.

Intelligence is the key to jobs and life, which means it’s important everywhere in life. If we can find real intelligence someday, maybe we won’t have to go to school and instead just get some vaccines and your school days are over. But being a quick learner is sublime too.

]]>On the soft snow

The lights I see

are forever beautiful

I stared at the empty space

What is really in

Those nothings

I don’t even know

What nothingness is

Because nothing is nothing

But is it nothing

Or is it space?

What is space

And what is nothingness?

If you were to zoom in to nothingness

What would you see?

Nothingness?

Or something sinister or secretive?

Maybe a secret to life?

Or just space?

What will we learn from space

The real final frontier?

]]>To see if it’s locked

I walk down the stairs

And see the busy docks

Seeing the cars roar by me

The loud noise of the buildings beside me

Calling for an Uber taxi

Riding in the Toyota back seat

The buildings are mountains waiting to be climbed

whether by elevator or stair

Then I see the city’s Mount Everest

I gape my mouth and stare there

It’s a wonderful world in the city,

Like no other experience ever

No words can describe what you see

I’ll remember this forever.

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