In every theory, certain tools are indispensable. Chaos theory is no different, and without phase portraits or phase space we would be dead in the water.
Every scientific road needs applications. Chaos is no different, and some led to further insights into the discipline. Here are a few of them...
Complicated? Yes. Possible to understand? For sure. Surprising results? Of course! The road to chaos is mapped here.
Calculus! We all love it, but who were the early pioneers that led the fight over indivisibles, a cornerstone for this topic?
We all love a good stellar mystery, and Tabby's Star is proving to be a great one. What possibilities exist for its strange behavior?
Like all important fields of study, Calculus had its growing pains. Here is the journey to the foundations of that amazing field.
None of us will make it to another star system. But that doesn't mean we can't see what one looks like. Starshot is that chance.
So many different versions to consider. Will you be the one to come up with a new solution?
Sounds made up, doesn't it? But in reality, it could be a missing key to physics.
Seeing other stars up close? Is it possible? Indeed! Come and see what was once science fiction!
New celestial objects in the solar system are always intriguing. What are these new classifications and their implications for us?
Black holes are engines of destruction unlike anything we are familiar with. One of their specialties is a tidal disruption event, and here we will delve into the mechanics of it.
Another one? Yes, a brand new field of study into how certain stars end their life.
While we don't know if they exist, the physics of tachyons would bring much excitement to science. But what are they?
Black holes are eternal, right? Nope, and the reason why is shocking: quantum mechanics!
Much happens here, and at a fast pace. Take a look at what you are missing!
Can such a thing happen? Many people in the past think so...
What started as a simple thought experiment grew to be so much more...
Why is the sky at night dark if stars are everywhere? Read on to find out the surprising answer!
Cosmological mysteries are numerous, incredible in size, and the possible explanations for them are just as bountiful. Let's explore the supervoid, one of those mysteries, and see what it could be...
Scientists have their own way to talk about black holes. Want to expand your ability to do just that? Read on to find out how...
Galileo, the great prototype for all scientists, made many discoveries in physics and astronomy. But whose work did he build off of?
Often a headache, time paradoxes are hard to fully delve into. Lets try and take a look at a few of them and see what we can learn from them.
How do we measure the distance to far away objects? A tough talk for sure, and the history behind the theories involved are just as interesting.
Sounds crazy, I know. Read on, for you may be surprised by what you find.
Ready for some ancient thought experiments? The solutions are not always as easy as they seem!
Another astronomical mystery without an easy solution. Did astronomers find an unknown planet in the 1830s?
Already a complicated subject, black holes get even weirder when viewed through the lens of string theory. Read on for some odd possibilities for what black holes really are.
The Inquisition was a dark time in human history. One of its victims was Galileo, the famous astronomer. What led to his trial and conviction?
Galileo was an accomplished man and the prototype scientist. But along the way, he got into a lot of verbal jousts and here we will dig deeper into the best ones he partook.
Astronomy is full of historical examples of mysterious objects seen but weren't really there. Did Lassell actually spot the rings of Neptune?
Galileo not only spotted new objects in the sky but also laid the groundwork for advancements in physics. What were they?
Galileo's findings in astronomy shook the world. What did he see?
Many objects have been seen in the sky that were found to be nonexistent. Here is one that was well-documented but alas, was something else...
The methods implemented by the ancient Greek people to find the circumference of the Earth were simply amazing, especially when you see how accurate they were.
Like many aspects of particle physics, electrons offer their own unique problems. Here is a sampling of some of the most interesting ones.
Captain Kirk had one last adventure after the Nexus. What happened that changes our view of his final mission? Read on to find out how he accomplished this feat.
Captain Kirk goes through an amazing journey in The Star To Every Wandering, not just physically but emotionally as well. Let us take a look at what new revelations we find out about Kirk.
Such a small difference can make a huge impact on physics. The neutron has done that, and a resolution to this problem isn't going to be easy to find.
Through this trilogy that celebrated the 40th anniversary of Star Trek, we looked at the inner psyche of Spock in a brand new light. Here we will examine him and how he was after the loss of Kirk.
In the first review of this novel, we saw Spock lose his control and reject his humanity. Here we will explore how he regained it with a little bit of help from an old friend and the impact it had.
A time of turmoil in the solar system, much evidence is found for its lasting impact. Here we examine that and see what conclusions we can reach.
Well before the rigors of science took hold in the world, people have come up with some creative ideas for our solar system. Let us explore a few of those now.
With an amazing trilogy to celebrate the 40th anniversary of Star Trek, breaking it up to examine its revelations is difficult. Let us take a look at what happened to McCoy in our timeline...
The start of the 40th anniversary of Star Trek provided us with an inside look at McCoy, a man who we find led two extraordinary lives. Here are some inside moments into the alternate life of McCoy.
Astrophysics has provided us with countless wonders in the Universe. Here is the next one though, and detecting one will prove to be more than a challenge.
Like the chicken or the egg debate, this has two sides that are determined they are right. Here is the evidence we have, and no easy answers are to be found.
Before New Horizons, little was known about Pluto's moons. Now, we are witnessing a complex picture forming around them that will intrigue for years to come.
The matter around you is composed of atoms but if we delve deeper we can find subatomic parts made of quarks and gluons. But they don't work according to our current understanding of physics.
Talking about the early Universe is a difficult proposition, with so many competing factors we have to take into account. Then throw in inflation, black holes, and holograms and we got complexity.
X-rays are a great tool for science, and so are lasers. So combine them and what do you got? Some awesome physics.
Finding the age of the Universe is like completing a puzzle without knowing the big picture. We have many clues, but sometimes pieces can be misleading...
Known for centuries, these mysterious particles are just now beginning to shed their secrets.
This little moon of Saturn is proving to be a fascinating place...for life?
Einstein has been verified time and time again. Want another test or two? Then let us push it to the extreme just like Gravity Probe A and B did.
Mercury is not only the first planet in the solar system but the least understood terrestrial planet. That all changed with the arrival of MESSENGER, and the secrets it uncovered are mysterious.
Many probes have visited our closest neighbor so many times. But so rarely has a duo been utilized for such precise measurements. Read on to see what Ebb and Flow uncovered underneath the moon.
An awfully subjective topic, but take a look and see if you find something you never knew existed. Our solar system has plenty to look at.
Another recent development in astronomy, though this one is full of mystery. What are these bursts and what implications do they raise?
Despite what you may have been told, we can see around a black hole if the conditions are right. Based on what we find there, we may have to rewrite the books on relativity.
Often in science, background workers put in the true efforts that other take credit for. Here is an axample of such an individual.
Some require little science while others are pushing boundaries. Here is a sampling of all the different methods we know.
While many points have to be considered, one swiftly finds themselves lost in the nuances of Chiron's properties and characteristics.
Not a frequently talked about subject in popular science, these objects may offer more to our knowledge of the universe than initially thought.
Figuring out how the moon was created is one of the deepest mysteries of archeological astronomy. We do have ideas though...
Though still mysterious, this hot field of science may be the keystone to physics or send it spiraling into chaos.
Everyone has heard of the Big Bang Theory, but what about possible alternatives? Read on to learn more.
What started as a simple verification of a long standing value in particle physics may hint at new possibilities unknown to scientists at this time.
The first landing on a comet proved to be more of a challenge than anyone thought it would be, but the science uncovered has been monumental and justifies the struggle.
Not something we think about often, but these waves would solve many problems in physics. Now, how to find them...
We all thought we knew what glass was. But recent developments have changed their purpose and now have placed them at the forefront of innovation.
Oftentimes in science, we encounter boundary objects that push the theories we have to the brink. Take brown dwarfs for example. Planet or star? You be the judge.
The return of Comet Halley in the 1980s sparked a huge spike in comet science. None was as successful as Giotto, the ESA's mission to explore multiple comets.
This is becoming more and more of a problem as urbanization rises, but we can learn from past efforts to influence our future actions.
Though not as popular as SpaceX or Virgin Galactic, this space company hope to use established technology to drive the private space industry.
Gravitational lensing is a bizarre consequence of relativity. This natural occurrence can reveal the beauty and science of some rare objects.
Easily a favorite topic amongst many of us. Now, here are some more reasons why we love lasers. As if you needed any more!
Though a fast-paced mission, this was a big step for later missions like LCROSS and LRO, and the science achieved here had implications we see to this day.
Though largely abandoned, the idea of a missing planet or asteroid field between Mercury and the Sun continues to intrigue us.
Not necessarily the first place to go looking for one of these features, to be fair. But that is okay, for the mechanics of this one are truly noteworthy.
So many space missions are never realized because of finances, politics, or technical limitations. Galileo somehow faced all of these and came through with some amazing science on Jupiter.
While there were many misses in this field, they deserve recognition as steps towards a sound method for exoplanet hunting.
With such extreme physics already at play, can we hope to understand the process behind black hole mergers?
While they are powerful engines of destruction, the beams they shoot into space are a separate breed of chaos which deserves a closer look.
After nearly a decade New Horizons has accomplished its primary mission of examining Pluto. What secrets did it uncover?
The mysterious dwarf planet Ceres captivates us as it presents new findings which challenge our theories thanks to data from Dawn.
All great space missions have a target. But Dawn is unique in that it is the first craft to enter orbit of one then leave it for another. Here is the story of its visit to Vesta.
Though a thorough list of movies would go on forever, it is possible to look at the Hollywood approach to black holes and learn what they got right—and absolutely wrong.
Science is all about remaining as objective as possible while developing new theories to explain other ones. So when science moves away from being empirical, problems arise.
While the current IAU definition is a good start, it needs revision and this system I propose may be a good place to start.
Thought by many to be engines of destruction, the act of consuming matter may in fact bring about creation.
Often considered a different state of matter, the BEC reveals many interesting physics of the bizarre.
All boundaries reveal new phenomenon and these are no exception. Learn the odd physics of neutron stars, pulsars, and magnetars.
Some of these tips may help you get across to a student and help them succeed in their subject!
Hopefully this article will help you recognize and fix your proportion mistakes!
These are easy-to-do tips on helping you save some gas (and money)!
While still going through growing pains, SpaceX is sure to be the best future for private space travel.
Once a mysterious point of light, but now a wild world full of surprises.
Much is discussed about Saturn and Titan, but the minor moons of Saturn deserve their moment in the spotlight.
Photons are hard to understand. They are even more challenging now after these newest discoveries which are analyzed here.
With the right tools and an ability to open up to new horizons, you too can delve into the mystery that is known as a quasar.
Though something we cannot hold in our hands, we may feel time slip away. But what is it? And after all is done, do we want to know?
If you haven't been in a fender-bender, consider yourself lucky. This article is about what happens when such an incident happens - in space!
These particles are a huge component of modern particle physics, but boy are they a pain to comprehend!
Recent work has brought up the question of the multiverse. Gravity may be the key to finally settling this debate.
Pluto was the forgotton planet (when it was still one) during the Voyager and Pioneer programs. Now, New Horizons will shed light on this strange object and its neighborhood.
Not many Americans remember the early struggles of NASA including its rocket failures and the USSR, but with Mariner 2 the US finally scored a first in the important space race.
Some objects get glossed over when it comes to solar system exploration. Now two important asteroids are finally getting their chance to reveal their secrets thanks to this special space probe.
Many of us are familiar with the Big Bang theory for the evolution of the universe, but many remain unaware of a competing theory that was more widely accepted in the 1950's than the Big Bang.
We know of many missions sent into space, but what about those special ones that came back with something from outer space?
Considered by Einstein to be his "greatest blunder," it in fact may describe the mysterious expansion of the universe.
The rotation of the material around a black hole is just a visible spin. Beyond that, special tools and techniques are required to find out more about the spin of a black hole.
Involving many principles of science, this particular paradox follows a consequence of black hole mechanics and has far-reaching implications, no matter what the solution is.
Though it lies 26,000 light years away, A* is the closest supermassive black hole to us. It is therefore our best tool in understanding how these complex objects work.
Now that NASA is no longer able to send astronauts without help, it is the age where the private sector is beginning to step up and provide new opportunities in space.
Though no one knows for sure where the water on Earth came from, many look to comets for answers. But are we looking in the right place?
These proofs go beyond the standard properties of the dot and cross product and explore new applications and surprising results.
With the use of the cross product, vector calculus really takes off, exploring new ideas and concepts that would otherwise be denied to us.
Having the appearance of the cross and dot products, the TSP instead offers a way to find the volume of shapes and more.
Vectors have components that may overlap other vectors. We are interested in these projections for various reasons, and their proofs offer further insight into vector calculus.
The mysterious dot product has a basis in vector theory that has wide applications. Here we examine how we know what it is and how to use it.
Unit vectors tell us the basic information of a vector. It is critical to know all the properties and proofs that help guide what we can do with them.
Vectors are an important component of higher-level calculus. How do we arrive at many of the results that we take for granted?
Throughout history, many famous contradictions in arguments and theories have arisen. Some have easy explanations while others leave one wondering how to resolve them.
Both of these are used frequently in astronomical work but the differences between them help us learn more about their sources.
How long is a day? Depends on what type you are referring to!
Remember that math class that had all the proofs? It had some strange facts in there also.
One will be surprised how some "simple" constructs around us are anything but.
While it may ultimately prove to be wrong, scientists know of several ways to test for string theory using many conventions of physics.
No one knows for sure how the solar system formed, but a possible answer lies in the Nice model.
Water is essential for life as we know it, so where we find it life could exist. But where in the solar system is water located?
We now know that water is definitely on the moon, but how did it get there?
We all know the pull of gravity that the Earth exerts on us. What we may not realize are the unforeseen consequences that range from our everyday lives to some strange hypothetical scenarios.
Though it works great on the quantum level, we have yet to see this work on the macro level. Is gravity the key to solving this mystery?
Though a brilliant object at night, the Moon can also be seen during the day. Even against the bright Sun, you can witness many of its features. But how?
Though it may be hard to imagine a world without the moon, many have dared to wonder. What results from its absence has more profound effects than we could have known.
When we look at the universe as a whole, we attempt to find anything that can be thought of as symmetrical. These clues reveal much about what is all around us.
Looking up at the sky, it seems so close and within easy reach. Man has landed there 6 times, and then never again. Why?
Oftentimes, we may encounter difficulties evaluating arguments. With the ability to translate these arguments into logical form, we gain new insights into their applications and implications.
Repeating decimals and terminating fractions can seen foreign to us and hard to utilize. But for certain ones, they have a relation with 9 that makes them easy to solve.
Truth tables have many applications in logic. Making one though is a challenge. Frequently, we will find many strategies that can help us turn arguments into truth tables.
With the use of material conditionals (if...then...) and bi-conditionals (...if and only if...), symbolic logic really begins to take off in practicality.
Knowing what it means to be truth-preserving, logically valid, having a sound argument, and how much inductive strength your argument contains can all be hard to pin down. That is, until now.
While often a useful tool in our math class, how many of us know why it works? Here is that reason.
Black holes, mysterious objects of the universe, have many different types. Do you know the differences between them all?
While we all enjoy a good bowl of popcorn, few know of the mechanics that cause popcorn to form in the first place.
Amazingly, under the right conditions a group of atoms can behave like an individual atom and become a superatom.
The eighth planet to be found, Neptune's discovery is full of politics and failed potential yet one of the ultimate triumphs in mathematical astronomy.
Though many know of the Space Shuttle, few know of the Orion Space Program. This rocket that failed to get off the drawing board utilized a unique fuel source: nuclear bombs.
This space observatory got its roots in a hidden frontier of light, and now continues to make advances into the x-ray world.
Though Pluto is no longer a planet, few know about the deep-space objects that were found which sparked that change.
Our world will run out of fresh water if we cannot find a way to purify other forms of water. Using these hydrates, a means to provide drinking water anywhere is achieved.
Dark matter and dark energy are still huge mysteries in astrophysics. Alternate theories exist to help explain them.
Inspired by its predecessors, the Cassini-Huygens mission aims to solve many of the mysteries surrounding Saturn.
According to current physics, equal amounts of matter and antimatter should have been created during the Big Bang, but yet it was not. No one knows for sure why, but many theories exist to explain it.
Though a space elevator, we can have safe travel that relies not on rockets but on simple physics.
Through the use of negations, conjunctions and disjunctions in logic, we can build up to De Morgan's Laws, a very powerful tool in logic.
These two rules in symbolic logic help us make far-reaching conclusions about everyday problems.
Frequently in philosophy, different papers can have common threads. These two philosophers have plenty of common ground that they both work on in an effort to uncover what truth is.
Authors frequently build upon their works. This is especially true for philosophers, and Quine's works on pragmatism clearly demonstrate this.
"Pragmatism and Humanism" and "Pragmatism and Common Sense" have many themes in common, building upon one another to create a new worldview.
Though it may seem unlikely, these two philosophy papers have much common-ground and build upon one another.
Though not a problem we all think of, we are running out of helium. What can we do about it?
Known for the ability to find alien worlds, the Kepler Space Telescope has changed our way of thinking of the universe. But how was it built?
Though both are ways to talk about groupings in the sky, galaxies and constellations have many distinguishing features.
Through famous for his namesake, the Kepler Space Telescope, Johannes Kepler is more renowned for his Three Planetary Laws. It was through the proof of the First that his skill was made plain.
Now a commonly-accepted object, black holes were for centuries a hypothetical singularity. So how did we discover the first one?
Though we all know how to use the Pythagorean Theorem, few know of the many proofs that accompany this theorem. Many of them have ancient and surprising origins.
These numbers are an important concept in mathematics and are key to understanding real quantities.
Though they may seem to be similar concepts, many features make matter and antimatter different.
The possible gateway to interstellar travel, warp mechanics govern how this will be possible.