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November 2, 2016  

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Imaginary Numbers: What the heck is it really?? How can a number be imaginary?? Well friends, let me tell you, on this Halloween Night, they are real. There are INDEED numbers which are considered imaginary. They have very special properties which do not exactly line up with what one might consider the "conventional" theory of mathematics, but is now so embedded in it, that it matches theory to a T. Quantum Mechanics cannot be described without imaginary numbers. So what are they?? Well, imagine this. What is a square root? A square root is a number which, when multiplied by itself, equals another number, it's square. So, the square root of 4 is 2. 2 multiplied by 2 is 4. The square root of 16 is 4. 4x4 = 16. Numbers whose square roots are a whole number are referred to as perfect squares. Now, let's consider this. Consider negative four. -4 times -4 = 16. So, the square root of 16 can be either positive or negative four. For the most part we forget the negative, since it's usually most practical to use the positive number. However, it does lead to a complex situation, there are no square roots for negative numbers??

That's kind of a pain for lots of calculations, and actually limits the boundaries of physics and mathematics. So, they came up with a solution. It's an imaginary number, called i. i stands for imaginary. Now, if you square i, you get negative 1, the square root of -1 is i. This allows us to have the square root of a negative number, which happens from time to time in calculations. What does that mean in reality? Well, there are what are known as real numbers, any number, positive or negative with any number of decimal points, finite or infinite. Then we have imagiary numbers, which gives us literally infinitely more numbers. It's also possible to have a 2-D plot of numbers, real on the so-called x-axis, and imaginary numbers on the y-axis, which means you can now plot a combination of these numbers. So there you go for Halloween, some spooky imaginary numbers. 

Next up: multiple infinities. Infinity is the biggest thing ever right? Wrong. Turns out, there are different infinities, each bigger than the next. This was in the mix for hundreds of years, but was finally set in place by Georg Cantor, in the late 1800's. So can it be? Well, all of these talks of multiple infinities starts in a field of mathematics called Set Theory. I actually took a Set Theory course in college, just to understand how this whole multiple infinities thing works. Let me tell you, while being very, very exciting, at the same time, it is very very complicated, and tedious. So tedious and literally insane that its father, the aforementioned Georg Cantor, went insane several times, spending much of his later life in insane asylums. He also had many detractors, including the incredible Henri Poincare, who said that his contributions were a disease infecting the discipline of mathematics. Unfortunately, Cantor turned out to be right. I think Cantor and Kurt Godel, with his incompleteness theorem, were like the two most famous hackers of mathematics. They just take this wonderfully, painstakingly logical structure, hack inside, and just bring it to the ground, with the implications of what they discovered using the rules of mathematics. 

So let's first simply consider integers, i.e. whole numbers, no decimals, negative and positive, so in the positive direction we have 1,2,3,4.... on and on, and in the negative direction we have -1, -2, -3, -4...and on it goes. So there are an infinite number of integers, right? However, we have developed a system where theoretically, given enough time and resources, you could count them all right? We know how to order them, and how to count them. This is what is referred to countably infinite. You know that after 100,000, the next number is 100,001. And on and on. Now next, we need to consider all the numbers which have decimals. Even just 1.1, 1.2, 1.11, 1.12, numbers which are referred to as rational numbers, as in having a repeatability to their decimals, feels a whole lot bigger a whole lot faster. Now let's consider irrational numbers, like pi, and e, and any other weird number which repeats on and on in no pattern whatsoever. These are referred to uncountably infinite, meaning that there is literally no way to count them all. And, if you took each number like this, and put them inside of a bracket, like [1.2123124124124, 223.2342938414234....,43.1234124,....] this is referred to as a SET of numbers. Now, the SET of irrational numbers simply between 0 and 1, is more vast than all the countable integers, and this is how we arrive at different levels of infinity. So, every time you think you have a bead on the universe, it will throw you a curveball and send you flying out in some other direction believe me. 
September 20, 2016  

Finally the complete episode....head on over to for the embedded tweets referenced in this podcast episode. 

September 18, 2016  
Alright friends, 2 weeks into the year for most of you, it's time to get back into it. Included here are 5 older episodes of this podcast that you really shouldn't miss out on, and are great for getting you back into the semester.

Episode 024: Sines and Cosines by Counting to 4!

Episode 063: 5 Critical Vector Properties for Components and the Importance of Coordinate Systems on Vector Operations

Episode 080: Physics Review Brushup Vol. 01

Episode 081: Physics Review Brushup Vol. 02

Episode 082: Physics Review Brushup Vol. 03

Also, check out the article from the beginning of the show right here.

Here's the CNN article about the last Full Moon of the Year.

September 11, 2016  
So this is the third in a three part series about my excursion to Brookhaven National Labs to tour their facilities for 4 "Summer Sundays" Sessions that took place during the month of July. If you're just tuning in, I encourage you to go back to PWN E091, just two episodes before, and start there, to get up to speed. We'll be here when you get back.  

It's kind of weird, but there was definitely something that kept me coming back to BNL this summer. Again, this time, the kids were in tow, so the main attraction, the tour of the RHIC, or the Relativistic Heavy Ion Collider, was off the table, but I didn't care. There's just something about the atmosphere and attitude of this place that I had to get my fill while I could.

So what was available, you ask? Well, first on the docket was a trip to the cafeteria. It was at this point that I passed a table where, apparently, if you attended 3 of the 4 weeks, you were able to collect either a coffee mug or a shirt. I had attended 3 of the 4, but with no evidence to prove it, and the lady there being a stickler for the rules, I emerged empty handed. (An insider, however, did hook me up with their coffee mug, which I now proudly display on my desk!)

So, what was left for 2 kids and a physics junkie who can't tour the RHIC? Well, of course, a trip to the demos of grad students. These were seriously cool, although the grad students were too high level for the attendees, IMHO. One showed me an electromagnet, and explained it to me in very high level terms, which I was able to follow, but was probably lost on the rest of the audience. He was able to, though, create a magnet with 4 poles, and could then change the poles at will by swapping the direction of the current, which he did via various switches. Putting a compass in the middle showed that it was swapping every which way, a very cool effect.

My final Summer Sundays experience was the theater show, this time by a man with grey hair, maybe in his late 50's, mustache, and beard. He looked like one of the quintessential tough guys out of the fifties, one that maybe you would expect to ride a motorcycle. What he did instead was present, extremely effectively, basic physical concepts to the audience in a way which was riveting to someone even my age. 

These are the three things which I remember the most from the presentation: 1) He threw the 3 and 4 pronged boomerangs made out of styrofoam around the stage and explained that if you threw them at a slight angle, they would always come back. He then explained that if you made an X shape out of a pizza box, with small trapezoidal shapes at the end of each "arm", you can make your own boomerang. He then proceeded to do it in front of us, making a boomerang out of corrugated cardboard. Fantastic.

The next part of the show which I remember was him using an actual bullwhip, and explaining that the crack of a whip is actually a sonic boom, and he then proceeded to make somewhere in the area of 30-50 of them. It is truly marvelous to hear such a thing in real life. He then took some matches and held them in his hand, and proceeded to use the whip to actually generate the force to break them. And did so several times until they were broken all the way down to his finger tips.

The last presentation he did was with bubbles, which seemed sort of childish to start, but may have been the most fascinating. He made huge bubbles the way one would expect, with the large hoop, but was able to make bubbles within bubbles, and finally, used a small straw to make hundreds and hundreds of small bubbles, something I had never seen before. He then made a normal size bubble, took the straw and was able to puncture the bubble, and blow bubbles inside if it. Visually fantastic and a great closer to the show.

Wish I could have seen the RHIC, but I'm guessing that each year the items are roughly similar since the nanotech, RHIC & light source are the 3 major items on campus, so I'm excited as all get out to catch them next year. And that does it for my trip up to BNL! Hope you enjoyed!

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August 31, 2016  
So this is the second in a three part series about my excursion to Brookhaven National Labs to tour their facilities for 4 "Summer Sundays" Sessions that took place during the month of July. If you're just tuning in, I encourage you to go back to PWN E091, just one episode before, and start there, to get up to speed. We'll be here when you get back.  

So, this time, when I went, I brought my mom and my friend who were visiting, and my 2 little kids. Because of this lineup, I didn't hit the lecture. When we got there, first thing we did was go to the cafeteria and hang out over there. Lovely nice open space, with a very friendly staff. Everything at this place is so laid back I love it. And the prices are very reasonable as well. I guess this is where the employees go to eat, so they try and keep the prices down. 

From there, the purpose of this week was to feature their synchrotron light source. This system creates light by creating a beam of highly accelerated electrons, which emit light. This has applications in medical imaging, as well as a variety of other, one would imagine classified, applications. With this crew we didn't get to see the light source, but rather went back to the theater where I saw the magic show last time, and we caught the laser show. There was a guy there who was hired, i.e. not BNL personnel, and he was showing us laser light, and how if you shine normal light on a balloon nothing happens, but laser light is so focused, that if you shine the laser light from the laser show on a balloon for more than 2 seconds, it can actually pop it because of the heat generated. 

He also explained how the lasers in a laser light show work: there is a single dot formed by the laser, much like one would imagine in a laser pointer. If you move a laser pointer around quickly with your hand, as I'd imagine many of the listers have, you can make a line, or a circle. This laser show moves so fast it can create complex designs such as people, and actually even animate them because it moves so fast. They have three colors for the lasers, red green and blue, which when they all shine on the same point become white light. 

He then went into the laser show, where they showed popular songs and did neat laser animations for each. I'm posting the pictures for the laser show on twitter as well as on this blog.

After the show, we pretty much bailed out. I wanted to see the sychrotron, but again, the lineup did not permit, so we rolled out. What I did catch, which I would say is probably the lowest level in terms of the science, is still very engaging. I highly recommend catching this if you're in town on a Sunday in July.

Featured App of the Week: Exploring Mathematics: Sine and Cosine. Because light is a wave, in order to understand this, you need to understand Sines and Cosines. Check out the app as well as the podcast episodes on Sine and Cosine! Also a critical review for the coming school year!
August 30, 2016  
So this is the first in a three part series about my excursion to Brookhaven National Labs to tour their facilities for 4 "Summer Sundays" Sessions that took place during the month of July. So, one thing that I found out last year is that you are not allowed to go onto the BNL campus without authorization. I stopped by and asked if I could drive around, and I got a very stiff "no" from the security guard. I did not realize the gravity, no pun intended, of this facility. 

BNL is a very serious science research facility. They do classified level research, have a particle accelerator, and at any given time are trying to be hacked by someone. Security is paramount, and so for obvious reasons they don't want me driving around in my minivan to see the sights. However, for 4 glorious Sundays a year, you can visit and tour parts of this magical place and see what the scientists are up to, in very broad strokes. The first weekend is called "Family Fun" which I was unable to attend. The second week, which will be our focus today, was called "Exploring the Ultra Small", the science of nanomaterials. This particular weekend was different for me, because I attended it with adults, which I did not do for weeks #3 and 4. Because I was with adults, I attended a talk which gave broad strokes about nanomaterials. 

So, upon entering BNL, you realize just how huge it is. It's a 5200 acre campus. Just huge. After the security check, you get your visitors stickers, and proceed through to the visiting center, where they have some very nice demos setup. They also have a cafeteria, gift shop, and a table full of my favorites, freebees. I got several postcards, stickers, and a ruler, since the topic of the week was measuring nanomaterials. 

I didn't get very much time to explore this, since the talk was starting shortly and we had to hustle over to another building. Upon entering the room where the talk was given, I was nostalgically thrown back into my college days. It was essentially a college lecture room, complete with an overhead projector(!). The guy giving the talk was the director of the Nanoscience division. I hadn't been to a scientific lecture in some time, so I was ready to roll. However, I was mildly disappointed because just when I thought we were going to get into the meat of the talk, it was over. It was at this point that I realized that the bulk of the attendees of this were high-school level teens. They were gripped with his introduction, but that's probably all they were going to be able to handle.  

That aside, he touched on some very interesting topics, such as what nanomaterials are. They exist on scales which are 10^-9 meters (check out Episode 005 of this podcast if you're interested in units of measure) The really cool thing to take from this section of the talk is that apparently what they're able to do is form nanomaterials "naturally", i.e. not using a small pointer to move around atoms. Take the sand on the beach for instance. As the waves wash over the sand, it forms specific shapes and there's nothing that we as humans have to do in order to get the sand to look that way. So, by the same token, is it possible to have a process like this which will assemble molecules in a desirable way that can be useful to humans and scientists for research? Apparently the answer is yes, but that's where the talk ended. This process is known as "self-assembly" and is evidently a cutting edge technology right now. I would love to learn more about this, and I think a lot from this talk will wind up as words of the day on PWN Physics 365.

From there we headed back to the visitors center where a Magic Show was starting. We headed in, and they did some really cool magic tricks, which were essentially science experiments which were disguised as magic tricks. The lady doing the magic was very engaged with the high school students, and the students impressively knew the answers to most of the tricks. One that stood out to me was that the lady had a balloon, allegedly empty but when she placed it on top of a tube, it self inflated and then popped. As the kids guessed, the balloon contained baking soda and the tube vinegar, which reacted causing the production of gas which "magically" inflated the balloon. Obviously, I was not the intended audience for this show, but it was fairly interesting nevertheless.

One last thing. I couldn't help but notice how many parents with Asian and Middle Eastern backgrounds had brought their children to this event, and how few "American" looking folks had turned out. I don't mean this as a slight towards them, but rather a compliment. It's very easy to see where these cultures place their value. They place it in education and learning, and when they take their children out, they don't take them to be entertained, but rather state-of-the-art science facilities which expose their kids to the latest scientific discoveries. As America continues to place it's value on being entertained rather than contributing, it's no wonder we're falling by the wayside to countries whose cultures have a ravenous desire to learn and discover. I certainly will be following in their footsteps. Their children were very bright, and very inquisitive and curious, and took every opportunity to interact with demos, ask questions, and answer questions when asked. You can tell they have very bright futures ahead of them. 

I left feeling very inspired. The atmosphere at BNL makes you want to learn, and to work towards discovering new features of our universe. It also makes you never want to leave, which makes it not so easy when we had to take off. There was a tour of the nano-material facility which we missed due to time, but something that I will certainly check out next year. 
August 22, 2016  

What I've been up to over the last four months. Check out more at

If you're listening, thanks so much for tuning in. We're still going strong!

March 25, 2016  

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Pick up the app in question for only $1.99 at:

The wonderful day is finally here! We've come a long way and are finally finished with how to handle vectors. Let's wrap up by going through a tour of the new app.  The first thing you will come across is the welcome screen, and then the main menu which will direct you through everything you need for your introduction to vectors.

The first place you want to start is answering the question "What's a Vector?" Tap this to enter the what's a vector menu. You can then get detailed explanations for the following: What's a Vector?, Magnitude, Direction, ijkijk (a cool trick for unit vectors), the right hand rule, and a method for vector addition and subtraction.

Now that we're initiated on what a vector is, next we dive into the anatomy of a vector. Shown is a vector on a cartesian coordinates axis with 9 different parts of the anatomy, with detailed explanations.

Now that you understand what a vector is exactly, next we go into how to do dot and cross products, as simple step-by-step procedures, and then examples of addition, subtraction, dot and cross products!

Finally, we test your knowledge with a flash card review. We test the ijkijk concept, vector anatomy, and vector addition, subtraction, dot and cross products. 

As if vectors wasn't enough, we then encourage you to go beyond, check out the podcasts for deeper resources, interact with the team by giving comments and ideas, as well as seeing other apps that are available!

So, that is a quick tour of the Vectors app, and will serve to wrap up the section. Be sure to check out the app in the store by clicking the link at the top or bottom of the page. Good luck!

March 17, 2016  

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In today's episode we continue digging into examples concerning our linear equation y = mx+b, where m is the slope, and b is the y-intercept. Our fourth example involves finding the equation from a graph. As usual, coffee-stained notes below. Enjoy!
March 6, 2016  

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In today's episode we continue digging into examples concerning our linear equation y = mx+b, where m is the slope, and b is the y-intercept. Our third example involves some not-so-nice numbers, to show how it usually is in math, ugly numbers. Find the equation of a line with slope -0.36 and intersects the point (271,25). As usual, coffee-stained notes below. Enjoy!


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