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Gravitational Lensing: A Window into the Past

In August of 2014, a group of international scientists came to a landmark conclusion that has forever changed the field of astronomy. Using the telescopes "Atacama Large Millimeter/Submillimeter Array (ALMA)" and "Karl G. Jansky Very Large Array (VLA)," a team of international astronomers confirmed that the galaxy HATLAS J142935.3-0-002836 (or H1429-0028 for short) was in fact a pair of colliding galaxies from the time when the Universe was only half its current age. These astronomers from Heschel Space Observatory, ALMA, VLA, and other observatories around the world collectively confirmed this observation through gravitational sensing. Continue reading

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Technology Makes Us Emotionless!

If you’re anything like me, you probably often find yourself squandering your day away on the internet. One minute I’m working on my AP Literature essay, and the next minute, I find myself watching cat vines on Youtube. When we think of advances in technology such as new computers or smartphones, we can easily see how each new advance benefits society. But what about the negatives? Most people worry about a slow decline in human interaction, but is there any merit to that concern? A group of researchers at UCLA  decided to test the validity of the statement. Their results were staggering; increased usage of social media may facilitate a decline in children’s social skills! Continue reading

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This sentence is false.

Once upon a time, there was a great Greek philosopher. People called him Eubulides of Miletus. One day, Eubulides thought of a question, and he asked “A man says he is lying. Is he telling the truth or lying?”

red blue buttons 300x165 This sentence is false.
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Let’s first assume this man is telling the truth in saying that he is lying. By definition, his statement would be a lie, contradicting what we first established, that he was telling the truth. But if this man is lying, then he lies when he says he is lying, aka he is telling the truth, again contradicting what we first established, this time that he was lying. In both cases, the conclusions are contradictions. Therefore, this man is neither telling the truth nor lying, somewhere in the green area of the dichromatic truth scale. [1] This is a classic example of the Liar’s Paradox.

If you look at the title, you can see another example of the Liar’s Paradox. If “this sentence is false” is true, then this sentence is false. Contradiction. If “this sentence is false” is false, then this sentence is true. Contradiction again. This neither true nor false statement raises a strengthened version of the paradox.

“This sentence is not true.” [2]

Since this statement is neither true nor false, this statement must be not true. And this is exactly what the sentence itself states, so this sentence is true. However, the sentence originally was not true, but is true now. The paradox arises again.

The paradox can also be in a form of multiple sentences. For example,

“The sentence below is true.”
“The sentence above is false.”[2]

Assume the above sentence is true. Then the sentence below is true. Therefore, the sentence above is false. Hence, the above sentence is both true and false, but it cannot be. Now assume the above sentence is false. Then the sentence below is false. Therefore, the sentence above is true. The conclusion is a contradiction as well.

“The second sentence is false.”
“The third sentence is false.”
“The first sentence is false.”[2]

raptor pondering important paradoxes 298x300 This sentence is false.
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Assuming the first sentence is true, then the second sentence is false, therefore the third sentence would be true, and accordingly the first sentence is false. If the first sentence is false, then the second sentence is true, the third sentence would then be false, making the first sentence is true. In an even more complicated way, we see the paradox again.

All of the examples we’ve seen so far have created a self-reference or a circular reference, but does a Liar’s Paradox have to contain some sort of circularity? In a more linear but equally if not more confusing paradox, in 1993, Stephen Yablo proposed an infinite sequence of statements A0, A1, A2, …, where Ai is an arbitrary statement in the sequence, and all of the greater statements Ak (I.e., k>i) are not true. Since we have an infinite sequence, the circularity of the Liar Paradox seems to be avoided. However, the contradiction still applies. Say Am is true, then Am+1, Am+2, Am+3, … are all untrue. However, Am+1 also states Am+2, Am+3, Am+4 … are untrue. Since Am stated that Am+1 was false, Am+2, Am+3, Am+4 … all must be true. If these statements were true however, this would break the rule that Am just applied to them. So ultimately, in case you didn’t see it coming, we’re again left with the same obnoxious paradox, only in a more linear form.[3]

How do you feel right now after seeing all different types of the Liar Paradox? Overwhelmed? Mind blown? Or maybe even a little crazy? Well, no worries, the greatest dragon philosopher, Dr. McDragon, will help!2009 07 21 Page 1 This sentence is false.

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Citations:
[1] http://www.logicalparadoxes.info/liar/
[2] http://en.wikipedia.org/wiki/Liar_paradox#Explanation_of_the_paradox_and_variants
[3] http://plato.stanford.edu/entries/liar-paradox/#InfSeq

Science Diaries: The Monk who grew Peas

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Anyone who has ever taken a Political Science class will know what separation of Church and State means. It's no SHIELD-classified secret that historically, Science and Religion have not exactly been the best of buddies. But that doesn't mean that person cannot be deeply religious and still contribute to the Pursuit of Knowledge. Newton, Lemaitre, Leibniz and Descartes were religious men who did more to advance humanity than most of us will ever do in a billion years. So today, let's take road trip down the memory lane to see another intellectual genius, a monk who gets forgotten in the scientific community far too often.

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Gluten is Not the Bad Guy!

Gluten Free 300x300 Gluten is Not the Bad Guy!
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Gluten free diets are all the rage, and it’s likely you may have at least one friend that abstains from eating gluten. Everywhere you look, there are gluten free food options and many people are adhering to this gluten free lifestyle. Gluten has a bad reputation, but many may not even know what gluten is and why you should stay away from it. So what exactly is gluten and how does it affect your health?

Gluten is found in products such as bread, cereal, beer, pasta and even gravy. Basically anything made from wheat, barley, or rye will contain gluten. It is a protein made by these plants and is useful in helping food keep their shape, think of it as a type of glue.  It’s what gives bread its soft chewy texture. While gluten itself has no nutritional value, the food items associated with it are rich in the essential B vitamins, iron and fiber. So why would people choose not to this seemingly harmless substance?

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The Mozart Effect Demystified

What do my high school English teacher, author-musician Don Campbell, and the Baby Einstein company have in common? They all espouse the virtues of Mozart and his music on improving long-term cognitive abilities—and they’re all wrong. Okay, I admit that I, too, fell into believing that listening to classical compositions while studying helped improve intelligence in some way.

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Cellphones Planes

Can Your Cellphone Cause An Airplane Crash?

When you board a flight and the captain tells you to turn off your laptop, and put your cell phone on airplane mode, do you actually do it? Everyone who has been on a plane has deeply doubted that their iPad could actually cause a plane crash. The fact is, they’re right…and wrong. Here’s why: Continue reading

astronaut

“Open The Pod Bay Doors, HAL”: Why You Should Stay Inside Your Spacecraft

poole2 “Open The Pod Bay Doors, HAL”: Why You Should Stay Inside Your Spacecraft
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Remember that time when you were in outer space, rocking to some 80’s alternative music on an old tape player, trying to save a galaxy from annihilation? Haha, yea… neither do I. I did watch it happen in a movie once though. I was very confused as to why the guy wasn’t dead when I remembered…it’s Hollywood, baby. Which leads me to this article. How in the world can a human body survive in outer space? And here’s a hint, Steven Spielberg has nothing to do with it. Continue reading

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What Really Sucks is that Vampires are Real

Chances are you’ve either watched a scary movie about vampires or you’ve read about sparkling blood-suckers with fantastic hair.   Either way, as much as you’ve either wished them to be real or not real, the fact of the matter is vampires do exist. Sort of. Clinical vampirism, or Renfield syndrome, is an obsession with drinking blood, and it is becoming increasingly common.

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Run Faster to Make Your Brain Faster

 

Brain In Blue by SilverGryphon8 150x150 Run Faster to Make Your Brain Faster
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We're all told that exercise is good for us, but whether due to a lack of time and energy or just pure laziness, many people end up far from fit. However, with this new study from the University of Illinois, you can no longer use academics as an excuse: if you really cared that much about doing well in school and wanted to be smarter, you would make the time to work out. Continue reading

From: http://static.fjcdn.com/pictures/Justin_fb088c_2994654.jpg

Why do we have eyebrows?

Eyebrows. Those two (or one) thin (or thick) strips of hair located above your eyes. Have you ever wondered why you have them? Think about it. The human race emerged as a separate entity from that of its early ancestors, notably the apes. You are still technically a primate, and you share many of the same physical features as other primates. However, there is one stark difference between you and a gorilla. You are a lot less hairy. Throughout millions of years of evolution, humans quickly shed their outer coats but why did they keep the hair above their eye sockets? These seemingly insignificant patches of hair have many more uses than you might imagine.
fullbrows3 Why do we have eyebrows?
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We're not just basic.