Math Does Not Equal Calculating

I have one question for anyone who has taken, or is taking calculus:  Can you explain what a Limit is?

I have asked this question literally dozens of times to engineering upperclassmen and graduate students.  Every single time its easy to see from their tortured attempts at an explanation that they have no real idea what a limit is in calculus.  They can integrate problems left and right, but they have virtually no idea why they are integrating something or what its purpose is.  

This is a fundamental failure of math education in this country.  We teach people how to calculate.  We don't teach people math.  

The fact is, calculations are a thing of the past.  Virtually all calculations performed in real world problems are automated with computers.  If memorization is the lowest form of learning, calculating is the lowest form of math.  It teaches nothing of importance other than how to follow a strict process to solve an over simplified problem no one will ever see in the real world.  And after 12-16 years of teaching math, no one has an idea WHY they are doing any of the calculations in the first place.

So I'll let you in on a little secret that most engineers eventually learn after college:  your math classes, and most of your math professors are a waste of time.  Most engineers don't really "understand" math until they start using it in the real world.  They quickly realize their schooling left them totally unprepared for what really matters:  learning how to correctly APPLY math (which is only a tool) to real world problems.

So let me answer that first question for you.  What is a limit?  Well, what is the smallest number of sides any shape can have?  One side only makes a line, not a shape.  Two sides will either make one or two distinct lines, again, not a shape.  A triangle, with three sides, is the shape with the least number of possible sides.  Four sides?  A rectangle.  eight sides?  An octagon...and so forth.

So what happens to a triangle, if we keep adding sides to it...over and over and over again.  Well, there is a limit that you will reach where your are no longer changing the shape of the object in any meaningful way.  Any idea what shape you will be left with?

A circle!  So, as you start to add sides to a triangle, from originally just 3 sides, to an infinite number of sides, the solution you will be left with is a almost perfect approximation of a circle. 

THATS IT!  That is the meaning and reason behind a limit.  There is no magic.  No black box.  Its simply a math trick that will allow you to come as close as possible (the limit) to the true shape of a circle, starting with something completely known...a triangle.

(Of course, limits can be applied to all kinds of things other than circles and triangles...things that exist in real life...like imperfect curves or surfaces...)

Saying Goodbye to Humanity

My apologies for the dirth of updates over the last few months.  An infant at home and an unusually busy semester load will do that to you...

I felt compelled to break my silence by an update on Voyager 1 that I read over at Bad Astronomy recently.  Since I have been wanting to post about the Voyager spacecraft for a while, now is the perfect time.

Voyager 1 was a NASA probe launched in 1977 to explore Jupiter and Saturn at a distance never before possible.  After providing some of the most fantastic science ever about these two monster planets, Voyager 1 slowly became something altogether different:  the ambassador of the entire history of our planet.

Recently, Voyager 1 reached a zone astronomers refer to as the "Heliosheath".  The picture below helps illustrate where this area is.

Basically, this is an area of space around our solar system where the solar wind from our sun no longer blows.  Voyager 1 has now officially said goodbye to our sun forever.  In a few years, she will leave the Helioshealth altogether and become the first object from planet earth to ever enter deep, interstellar space.

Realize that with time, all things will end on our planet.  At some point, our sun will engulf our world, destroying everything mankind has ever accomplished.  All knowledge or memory of our existence will be destroyed and it will be as if we never were.  All the timeless monuments to our brightest and best,  Egyptian pyramids that have survived 4000 years,  the Great Wall of China...they will all be gone forever.   Hopefully we will have long left our tiny planet for greener pastures by this time, but at this point, we can only hope for such an outcome.  

No matter what our future holds, Voyager 1 and 2 will always go forward, with evidence and descriptions of our existence.  On board each is a gold record with detailed instructions.  Any intelligent species who encounters these probes could then hear greetings in 55 different Earth languages, listen to the sounds of our whales, dolphins and weather, even listen to our music.  Due to this spacecraft, we are guaranteed that for as long as the universe exists, our place within it will always be known.

Soon, we will have to say goodbye to our stellar ambassador forever.  One of Voyager's last messages home before leaving our solar system was a picture.  One of the most famous NASA pictures of all time.  If you have never taken the time to stop and look at this picture, you cannot yet possibly know what it is to live and breathe.  That pale blue dot is us.

No one has ever immortalized the meaning of this picture better than the late, great Carl Sagan.  After seeing this picture, not too long before his death, Sagan urged us all to look at this picture in awe.

"From this distant vantage point, the Earth might not seem of particular interest. But for us, it's different. Look again at that dot. That's here, that's home, that's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every "superstar," every "supreme leader," every saint and sinner in the history of our species lived there – on a mote of dust suspended in a sunbeam."  - Carl Sagan

Nothing else ever needs to be said...

A scrub for Copenhagen Orbitals

 

Tweeting from their home made submarine has confirmed their initial suborbital launch has been scrubbed due to a blocked oxidizer nozzle.  The oxidizer nozzle controls the flow of oxidizer on its way to mix with liquid fuel before combustion.  It is common with liquid oxygen as an oxidizer to have this nozzle "freeze up" and become blocked.  Usually, some kind of heating element is generally used to "de-ice" the nozzle before launch.  Rumor is those crafty Danes were using a simple hair dryer to accomplish this task.  This could possibly be cause of the failure.  Keep an eye on their website for further developments.

    Launch is most likely going to be delayed until 2011.

Asteroids: Should we really be concerned?

Please take a look at the following simulation.  Play it in HD so you can see the full effect.

This animation shows the number of known asteroids in the solar system that have been detected, along with their corresponding orbits.  The simulation starts in 1980 and moves to current day.

Watching Earth, you may notice that it looks like we already should have gotten hit many times over the past 30 years, however, this is a 2-D representation.  The asteroids that look like they are hitting the Earth are actually passing in front of, or behind our planet.

I'll let you make up your own mind...

The Engineer's Dream Lives: Copenhagen Suborbitals

Look at this picture.  What do you see?  I see a rocket, a water launch pad and a submarine.  Obviously, the submarine is towing a rocket and launch pad out to sea for liftoff.  Who would be undertaking this endeavor?  North Korea?  Iran?  Some other sovereign nation?  Maybe a company?  A large defense contractor somewhere in the world?

The answer is none of the above...all of what you see has been 100% built by hobbyests.  While you and I tinker with our cars in the garage, or add on to our houses, these guys were building a freaking space rocket.

Oh, and that submarine?  They built that too...that was last year's project...and its been to the bottom of the sea off the coast of Sweden quite a few times...they named it "The Nautilus" ofcourse...

It really is impossible not to be impressed by what engineers, on their own, with no management, company or government backing can do.  A typical defense contractor would probably charge billions to make all this...they built this test rocket with $70k.

In 6 days they will be launching a test dummy into suborbital space, hopefully a human in 3 years...the same feat Burt Rutan pulled off a couple of years ago...Keep in mind, Rutan's Scaled Composites is a company, which has received significant funding from the US gov that enabled it to exist in the first place.

These guys work in a shed.  On their own time.  Why?  Because they freaking can!

A lesson all too lost in today's companies where powerpoint engineering is the rule, and actually doing, or making something, anything is deemed too big a risk.

These guys are an inspiration to engineers everywhere.  Will the rocket blow up?  Scrub launch?  Ditch in the ocean?  Be 100% successful? We'll find out in about 6 days...stay tuned...

More info on Copenhagen Suborbitals here.

Guest Post: Wilbur and Orville's Mom

Introducing fellow science diplomat Natalie Straup.  As we add more writers to this blog I will continue to update a list of diplomats on the right side of the page.  For a quick intro, Natalie is master's level mechanical engineer working for a major defense contractor.  Her post does a great job telling a mostly forgotten story of science and technology.



           The Wright Brothers


On this 90^th anniversary of the 19^th Amendment, let’s take a minute to talk about women in science and technology.  I must admit, I don’t give this topic much thought on a day-to-day basis.  However, I was talking to a co-worker about his recent summer vacation to the Outer Banks a few days ago when an ordinary discussion suddenly got interesting.  In particular, he was rehashing his trip to Kitty Hawk, the site of the Wright Brothers’ historic first flight.  He asked me if I knew that the Wrights’ mother, Susan, had been their go-to source for mechanical advice.   Back up a second – the Wrights’ mom?  What? 



      Susan Wright

After a little digging around, I found out that Susan was a remarkable woman.  It’s hard to imagine anyone, let alone a woman raising children over a hundred years ago, making her own appliances.  Without her guidance, it’s possible the Wright Brothers might never have employed the scientific methods that ultimately led to their success.  It’s equally remarkable that I’ve never heard this aspect of the story before.  There are several organizations for women in science and aerospace.  Our schools and colleges are scrambling to find ways to inspire tomorrow’s female engineers.  Even NASA and Mary J. Blige are teaming up to encourage women to pursue the sciences.  This is not a new concept – it’s been going on for decades.  So why aren’t we more successful at it?

Perhaps we’ve been holding up the wrong role models.  Amelia Earhart, for all her accomplishments, is best known for being the first woman to achieve what men had already done.  While that is certainly admirable, it’s not exactly awe-inspiring for anyone to follow in another’s footsteps.  Think about the top women role models we have today.  Not many that immediately come to mind are known for the ground-breaking work they’ve done to advance the fields of science and mathematics.  Sally Ride?  Humankind had already been to space.  Even the famed California Governor and First Lady’s Conference on Women has just one scientist speaking this year, among several journalists and actresses who will be taking the floor.

This is not to say that we lack examples of extraordinary women in technical fields.  Marie Curie is but one example.  If we truly want to get girls excited about science, however, we are going to have to do more to recognize the ground-breakers in our midst – whether they shine in their own spotlight (in Mrs. Curie’s case, she glowed) or they are the driving force behind those who do, like Susan Wright.

So go call your mother and tell her thanks.

More on Susan Wright

The Greatest Dispute in Science, Part 2: The Fibonacci Sequence

In Part 1 of this series, we talked about the ancient mathematician's obsession with finding perfection in the form of a circle.

As it turns out, Pi is not the only important ratio ancient humans discovered.  There is another called Phi.  This number is approximated at 1:1.618, and much like its cousin Pi, its an irrational number with an infinite number of decimal points.  One of the important take aways from the history if Pi is that nature doesn't really provide us any evidence of a perfect circle.

This is why Phi is a much spookier number:  Nature does show us this ratio, and not just in one place, but in many places...large and small.  You find this ratio in the sunflower pictured above.  You can find it any tree near your house.  We can find in the limbs and lungs of our bodies.  We can also find it in spiral galaxies.  In fact, this one single ratio, this one number, appears to be everywhere almost as a cosmic signpost.

The Phi ratio is slightly harder to understand than Pi.  The following movie should get up you speed quickly with what Phi means.  Once you understand the ratio, we can talk about its implications more.



Now, no matter what you may think of the mystery apparent here, there is no doubt the ratio is real.  Its occurrences in nature are real as well.  It was here long before humans were; we didn't invent it, we discovered it.

Lets look at this a little closer from our  Chaos vs. Order standpoint.  It has been often said that the fibonacci number connects everything in the universe.  Unfortunately, when you really look at it closely, this is not really true.  The astute eye will notice a commonality in every instance of this number in nature.  Can you spot it?  Its natural growth.  Exponential natural growth to be exact.  We find this ratio only in instances where there has been evidence of some kind of natural growth.

Even so, while it is misleading to say this number exists everywhere and in everything in the Universe, the fact that is seen is just about all natural growth is astounding.  A galaxy 100's of millions of light years away grows at this rate.  The ratio of your forearm to overall arm?  There it is again.  The ratio between a tree's trunk and branch section?  There it is again.  Its also in your DNA.

The next video might point out the "Dan Brown" reality of the fibonacci number a bit better:



Where else might it exist?  There is a new branch of economics called "Elliot Wave" which tends to show strong past stock market correlation with the fibonnaci:



So what does it all mean?  Science really doesn't have an answer as to why this one ratio seems to govern all natural growth, aside from the fact that it tends to be the most efficient form of growth.  In this respect it appears nature tends to favor efficiency over chaos and randomness.

We'll rack one up for order.  Chaos 1 - Order 1

As an added bonus, even a well known rock band wrote a song all around the fibonacci sequence.  Once you understand it, it becomes quite a feat of composition:

The Science of Baseball

Single A baseball is about to end for the Grasshoppers this season.  To celebrate the awesomeness of minor league baseball, lets do a baseball related story.



All sports generally involve nothing more the physics.  For most sports, an athlete's job is simply to excel at physically using the laws of physics to control the motion of two simple things:  their bodies, and some sort of ball.  Football, Basketball, Hockey, Soccer...they all fall under this definition.  Even NASCAR meets this definition if you consider the "car" as being a "ball" that the athlete is still physically manipulating.

Some sports are simpler:  the basic sports.  Running and swimming are two examples of the simplest of sports...in these cases there is no ball for them to manipulate at all...they entirely revolve around the use of the athlete's body and nothing more.

Baseball and Cricket are different.  In a real, scientific sense, these two sports are simply more advanced than the others.  Why?  Contact between the bat and the ball.  The pitcher does his best to manipulate the ball, but he doesn't score any points by this act.  The batter is doing his best to manipulate his bat in order to hit the ball in the best way possible.  The skill or craft of the pitcher is entirely different than the skill or craft of the batter.  Where they meet is pure physics.

There are two things all baseball managers have a to be good at, statistics and physics.  Most managers probably need a masters level knowledge of statistics to maximize his team's change of winning an entirely different, and extremely complex situation every game played.

For the fun of it...lets look at an article in Discover about what science can absolutely tell us about Baseball:

1.  Most base-runners continue to take the wrong path running from home to first.
2.  Statistically, little brothers are strongly shown to take bigger risks than their older brothers.
3.  When home town advantage matters, it tends to matter due to jet lag.
4.  Being a night-owl or early riser can make a big impact on a pitcher's EPA depending on city.
5.  At the MLB level, its physically impossible for anyone to "see the pitch"...its really a guessing game.
6.  Batters may actually see a bigger ball (mentally, not physically) when on a streak.
7.  Want to see the benches emptied?  Go to a game on the hottest day of the year.
8.  Baseball favors lefties over righties overall.
9.  Conventional wisdom that youth pitchers shouldn't throw curve balls is wrong.

Check out the article here.

Relativity - A Primer

Einstein's first paper on relativity came to some rather mind blowing conclusions:

1.  Time actually slows down the faster you are moving (what?)

2.  The speed of light (C) is always the same relative to you...without regard to your own speed (your just crazy now...)

The fact is that the only reason these conclusions are so mind blowing, is that we, as humans, are very limited in the ways in which we can "see" stuff.  The old saying is that seeing is believing...but we all know this is not true.  If a tree falls in the forest and no one is there to see it, it did indeed fall (as can be easily verified by visiting the site after the tree has fallen).  This is true in all realms of science.  Humans can only "hear" a small frequency range of sounds.  That means there are all kinds of sounds happening around us at any given time that we are oblivious to.  But there is a chance those same sounds might be driving your dog insane.  Our vision is even further constrained to visible light in the fact that we can't actually "see" most of the light in the universe (while other species and sensors we have built can).

The same can be said for relativity.  The only reason the above two concepts do not make any logical sense to us is that we, as humans, have no experiences traveling at super fast speeds, and we have no concept of living on, or around super (and I mean really really large) masses.  The Earth is big, but its a grain of sand compared to other objects in the Universe.  But if we did live truly in the fast lane, on a space ship flying at the speed of light, or if we lived on the surface of a super massive object (like a collapsed cold star)...these ideas would be as normal to us as apples falling to the ground or the colors of the rainbow.

Below is an excellent primer on the ideas of Einstein's theory of special relativity.  I promise when we are done, you will be able to easily understand what relativity is and how it works...just like Einstien...and you'll likely have even more admiration for the man for the creative capability to imagine these natural concepts which elude our every day lives...

Rare Southern-US Aurora Possible Tonight

Turns out our sun "burped" pretty big yesterday.  This solar wave of energy should be hitting our atmosphere today (Aug 3).  Look up tonight, people in locations as far south as Virginia may get to see a very rare occurrence of aurora.

Watch the sun's "burp" here.

Science Journalism Failure #4,964 - The "God" Particle

Recently the scientific community has been all flustered with rumors that particle physicists are getting very close to discovering "The God particle". It seems journalists always need to coin some terribly misleading, patronizing, yet snazzy-sounding name to their headlines for fear that their story really isn't, well, "news" (they are right, most of the time).

Lets put a stop to this journalistic absurdity right now: there is no "god" particle. The particle they are referring to is the Higgs Boson, a subatomic, elemental particle predicted by the standard theory of particle physics that has yet to be discovered. There is nothing "godlike" about the particle. Its simply the last boson left to be discovered to complete the initial standard model as show below:

The neat thing about the Higgs Boson is it is supposed to give mass to the other particles. But there is no magic, god-like quality to this particle anymore than there is to the 4 fundamental forces of nature (gravity, strong nuclear, weak nuclear and EM).

Even IF this particle is found, particle physicists now believe the standard model is already outdated and additional particles would therefore need to exist in order to explain higher energy reactions (as described above). On top of this, the standard model still fails to explain gravity and relativistic physics (physics on a very very large, fast scale). Finding the Higgs Boson would be a great discovery for science, but it would be no greater than many other discoveries before it (Electrity-Magnetism link, Relativity, Gravity...etc). The engineering benefits to man-kind that would follow from finding this boson are murky, if non-existent at best in our lifetimes.

So at this point, should you care? Not really. It would basically be confirming a scientific model we have already been using for 50 years.

The Birth of US Space flight, 60 years ago...

A picture illustrating when and where it all began at Cape Canaveral. This is one of von Braun's v-2 designs the US "borrowed" from Germany post WWII.

Years later we will go to the moon and launch space shuttles all from this location...

(and no, NASA won't let anyone quite that close to the launch site anymore...)

The Best Science TV is not on Cable...

About 15 years ago, one had quite a few quality options for finding decent science entertainment on TV, mostly on cable. Three channels in particular became very successful over time: The Discovery Channel, The Learning Channel and the History Channel.

While the History Channel used to take a good amount of criticism as the "Hitler Channel" due to its over reliance on WWII topics, today's version of this channel, as well as the other two, are shadows of their former selves.

The Learning Channel is probably the biggest culprit for following MTV's lead of having content that has virtually nothing to do with its name and mission statement. While TLC used to have many quality astronomy shows, it now sports endless reality shows about "little people" and tattoo parlors. TLC, at this time, has virtually nothing to do with science or learning. Discovery and History have also falling to new lows with shows about crab fishing, driving trucks in Alaska and endless pseudo-scientific nonsense about aliens and Nostradamus.

But I'm here to say quality science programming DOES exist. Here's a list of online science programming that, in most cases, far exceeds what you will ever find on History, TLC and Discovery in terms of content, quality and entertainment. The production quality of these shows is easily on PAR with the likes of "Planet Earth" and "The Universe", with excellent HD video. I highly recommend viewing in HD as a podcast with your HDTV.

...and the best part! They are all free without the need for a cable subscription!

(My apologies to MythBusters, the only quality science show remaining on cable TV)

1. The Hubble Cast HD

The Hubble Telescope has been the scientific achievement of the human race up to this point. While the Apollo Project was Man Kind's top engineering achievement, we have learned most of what we know about the Universe through the eye's of Hubble.

2. Earth-Touch's Wildlife Highlights HD

Earth-Touch puts most nature shows on cable to absolute shame. Stunning HD photography, free from any contrived story lines or political biases (mostly). This show, along with its sister marine show should be at the top of every nature lover's list.

3. Earth-Touch's Marine Channel HD

Same as above, focusing on marine life.

4. TED talks in HD

TED talks are fascinating public lectures about the current state of technology, nature, science and our world. While the lectures themselves have agendas and political bias, the library of lectures through TED does not.

5. ESOCast HD

HubbleCast's younger brother, focusing on cutting edge-land based sensors in Andes mountains in Chile.

6. NASA's Jet Propulsion Laboratory HD

Cutting edge, high quality updates from the world of NASA. A must for NASA enthusiasts...

Enjoy!

The Greatest Dispute in Science, Part 1: A Perfect Circle

Today, I am going to start writing a series on what has become the largest battle in science history. This battle started brewing shortly after Einstein published his work on General Relativity and exists to this day. It is a battle that means everything for the human race, how we view ourselves in the Universe and in the end, who we actually are. You can see this battle occur everywhere, both within the world of science and between you and your friends and family. It exists at all levels of the human conscience:

Order vs. Chaos

I do not pretend for to know the answer, nor will I claim one. What I will do is discuss the fascinating battles and theories that have taken place over the years. The battles won and lost on both sides. While most of us make our arguments with books, religions, history and anecdotes; we'll be focusing on how science has waged these battles, the only place where solid evidence and the scientific method serve as referee to constrain the participants’ arguments.

We are going to start with something simple:

Humanity's search for perfection in the form of a circle.

If you ask the average person on the street what they know of π, you might get an answer of 3.14 from someone who either studied math or has a good memory. If you are really lucky, you might hear 3.1415 from an engineer or scientist. Many however, have lost sight of what π actually means: the illusiveness of perfection.

First of all, π is a number, pure and simple. It is not a formula and it means nothing more than the number it represents (3.1415…etc). Its simply much easier to refer to this inconveniently long number as an old Greek letter (anybody with a very long name can sympathize with early mathematicians).

Obviously, there has to be something special about this number, since its one of the oldest numbers in human history. Ancient Egypt and Babylon knew it was a little bigger than 3, but they couldn’t figure out the exact decimal representation. Over 2000 years ago Archimedes of Cyrus was able to figure out the best approximation of π which lasted until the 1800’s, when William Shank calculated it to 527 decimal places (in a time long before computers and calculators no less).

Why all this devotion to a seemingly random number?

Perfection.

You see, in order for a circle to truly be a circle, its MUST have the exact number of π describing the ratio between the circle’s diameter and circumference. My favorite graphical illustration of π is below:

You see, we can easily measure a circle's diameter. With the advent of flexible or clothe rulers (like the ones tailors use), we are also able to accurately measure the diameter of the same circle. However, unlike other basic shapes (squares, rectangles, triangles), these measurements do not easily provide us the area of the circle. For this calculation, we need π.

Area of a circle = π multiplied by the circle’s radius, squared.

Without knowing π, we can never know the true area of a circle. So it was important for mathematicians to discover this number so people could know things like land area for early circular shapes (coliseums…etc). Unfortunately, finding this number precisely, has taking the smartest human brains thousands and thousands of years to determine.

The end of this story is not a very satisfying one for many people: the exact number of π does not exist. In fact, the true amount of decimal places extends to infinite. Which in turn means humans can never make a perfect circle. We can never know the exact amount of area within a circle. Therefore, early mathematicians learned that in the case of geometry, the ultimate and most advanced mathematical tool of the day, perfection does not, cannot, and will never exist.

This ultimately makes sense in one crucial way: a perfect circle is not provided to us, anywhere, in the known Universe. No planet is perfectly circular. No orbit is perfectly circular. Nature, it turns out, might be a chaotic and haphazard place, the idea's of perfection and order were disappearing; A frightening idea indeed to most people in the ancient world.

The Smartest Man in Human History

That’s right I said it, but don’t take my word for it. Listen to Astronomer/Physicist and fellow science ambassador Dr. Neil Tyson discuss Sir Isaac Newton in this TIME special:

Much like Einstein’s famous E=mc², the reigning champion in the realm of famous equations prior to Einstein was Newton’s F=ma. An even more elegant and simple equation since there is no square involved.

Last time we provided an example of how to “read” and equation in English. Lets try this again with our second most famous equation in science history:

Translation: “The force (F) on any object must be equal to (=) the mass of the object (m) multiplied by the acceleration (a) of the object”

This may seem painfully obvious to you, but at the time, this was some mind-blowing stuff. Acceleration can be an abstract idea to some, so let's clear this up right now. Acceleration is a rate. It describes the change in velocity of an object.

Newton’s concept comes down to a firm base in position of where something exists in space. A simple concept that we all are quite used to. “My car is parked in the garage” is an example of a position of an object. You could also say, “my house is on 101 Newton Avenue”, but there’s a big difference between a car and a house: a car moves!

Since you car actually moves from time to time, its position must change. The rate of positional change of your car is known as velocity (or speed). If we take this idea one step further, we can determine the rate at which an object changes its speed over time. This rate is known as acceleration. A car cannot move without accelerating first, and it cannot stop without decelerating.

Back in Newton’s time, the distinction between speed and acceleration wasn’t very clear to most people and many actually considered them the same thing. Newton however, realized something amazing: of these 3 (position, velocity and acceleration) the human body can only “feel” acceleration. You feel the same whether you are sitting in your house or at work. If you were riding in a car on a perfectly smooth road with your eyes closed, you would not sense that you are moving at all! The only way to know you are moving would be using your eyes. However, when you accelerate or decelerate, you can “feel” it. Your body is forced into your seat when you are accelerating. A force therefore is something you can physically feel.

Newton correctly, and for the first time in history, realized that the force you feel on your body must be directly related to your body’s acceleration. Conversely, in order for an object to change is velocity (speed up or slow down), it MUST experience a force. Sometimes the force you experience is a bad thing…in a car accident, the force that hurts you is due 100% to how fast you decelerate to a stop.

But Newton also realized that mass plays a large role in this relationship because the heavier an object is…the more force it takes to speed it up and slow it down. So as you can hopefully see, there is something oddly fantastic about this because it describes something visceral and basic in your experience as a human being: the sense of physical feeling. Anytime you feel motion as a human being, you must be accelerating in some fashion.

Believe it or not from this formula, spawned forth all modern forms of travel, machinery, weapons, our understanding of the solar system, and even how we measure the passage of time! If it wasn’t for Newton, it might have been another 1000 years before this law of nature was realized, and we’d still all be travelling by horse, never going more than a few miles away from our homes…

...An interesting Newton Fact: The smartest man to ever live wasn't smart enough to avoid the 18th century's largest economic bubble when he lost over a million dollars (in today's money) when the South Sea Company's stock crashed in 1722.

He later remarked: "I can measure the motions of celestial bodies, but I cannot measure human folly."

Keep this in mind any time you here economists who believe they actually know how the economy works. If Newton couldn't figure it out, its doubtful anyone else can.

So just why is this Einstein guy famous?

Everybody knows this guy. It doesn’t matter if you are a scientist, engineer, musician, athlete or an office worker. Albert Einstein is amazing simply for the single achievement of becoming the “rock star” of scientists. The only other scientist to ever come close to his level of world wide fame might be Sir Isaac Newton (whom we will introduce next post).

So why all the fame? Do you know just what it was that made this guy so great? Sure he’s smart, but there are tons of smart scientists out there that are virtually unknown (in fact most of them are pretty obscure).

Here’s one reason:

E=mc²

One of the most simple and elegant science equations ever written. Only 3 letters (variables) and one is usually always constant (c). But why? What does this equation mean? Just why is it so important?

First off, since this blog is written for those with no science and math background, lets make sure we understand just how simple and easy a math equation is to understand. I know, most math equations look like greek to most people, but they are actually very easy to comprehend by anyone, way more easy than learning another language (the author is currently learning French).

So, lets start off by translating this equation into English. After all, every math equation is just another form of a “sentence” expressed in the language of algebra.

What this equation says in English is simple: All the energy (E) in an object has to be equal to the amount of mass (m) in the object multiplied by speed of light (c) squared.

(Notice how math reduced all that text down to three letters with no loss of meaning. This is one reason why math is considered the "universal language")

A “square” is a simple concept you learned way back in grade school. It’s a number multiplied by itself. So the square of 8 is simply 8 times 8, which equals 64. Here’s the deal, the bigger the number you are squaring, the bigger the total square is going to be. In this case, “C” is the speed of light, which is an amazingly big number: 671 million miles per hour to be exact. Think about that for a minute, how fast does your car go? This can only mean that when we square this number by multiplying it by itself, we are going to be left with one insanely huge number: 450,241 TRILLION. That’s a hell of a number. One that the human mind, even Einstein's, cannot truly comprehend.

So the basic idea here is that “c²” is big…really, really, really big. Now what happens when you multiply this huge amount with any other number (in this case, an object's mass)? Even if the number is very very small you will still be left with a huge number in the end.

So what this equation is saying is that there is a hell of a lot of energy stored in even the smallest amount of matter. So much energy in fact, that if you could release it, you’d end up with this:

That’s right, nuclear fission is the process of splitting apart a very small amount of matter (just a couple of atoms). Most of that matter is released in the form of “radiation”, which for our purposes is the same thing as energy. Light, heat, gamma rays, x-rays…etc are all forms of radiation or energy. We see the light and feel the heat from the explosion; we don’t see the huge amount of energy that is released as harmful radiation. But its in there.

This is what Einstein is partly famous for (we’ll get into some other cool things later).

But the basic understanding here, that everyone can easily understand, is that Einstein discovered a basic law of nature. A law that states that every little bit of matter that exists in the universe is actually an extremely dense form of tightly packed energy. A similar (but not entirely accurate) way to think of this is: matter is like energy that has been “frozen” down to a really small space.

Now, the next time you see a picture of Einstein, watch a video of a nuclear explosion or see the most famous equation in the history of science, you'll know exactly how they are all related and exactly what they mean. In fact, you now have the same understanding as a scientist...just with out a lot of the math that was used to prove it!

A sort of introduction.

Ask yourself a question: do you understand what the above two equations "mean"? I suspect for most, the truthful answer is no, which is a really good illustration of how we tend to fail at conveying science.

Recently, I read a story on digg and reddit that asked the following question: are you wealthier today than John D. Rockefeller (whom was worth close to 80 billion dollars in the late 1800's)?The truth is that, in almost every meaningful and measurable way...you are. The reason is not money, but time and the above two equations. You were lucky enough to born a little over 100 years later after engineers had some time to tinker with these equations...the benefits of which Rockefeller, despite all his wealth, could never enjoy.

Lately, "climate gate" has been a leading headline in the news. The following discussions that occurred made it clear that scientists have a problem. They have a very big problem: no one else can figure out what the hell they are doing, why they are doing it and why it matters.

Scientists are great at a lot of things. They are smart as hell. But one weakness just about every honest scientist confesses to in secret is that they are bad communicators. One needs only to sit in any University Freshman Physics or Calculus course to see this illustrated first hand.

That's why this blog exists. Being able to do the whole "math" thing makes life a bit easier I find. Bear in mind I don't consider myself to be "good" at math, and I certainly don't like it. Yet I have always found it somewhat easy to do and very useful. I tend to live in the layman's world, only temporarily hopping over to the ivory tower to check out whats going on. In this blog, my goal is to help you understand a little bit more about what these weird guys in lab coats are up to all day. When it matters, when it doesn't, and to delicately mock the journalism profession for endlessing screwing up their job in this respect.