Josef Prusa’s designs have always been trustworthy. He has a talent for scouring the body of work out there in the RepRap community, finding the most valuable innovations, and then blending them together along with some innovations of his own into something greater than the sum of its parts. So, it’s not hard to say, that once a feature shows up in one of his printers, it is the direction that printers are going. With the latest version of the often imitated Prusa i3 design, we can see what’s next.
Working with high voltage is like working with high pressure plumbing. You can spring a leak in your plumbing, and of course you fix it. And now that you’ve fixed that leak, you’re able to increase the pressure still more, and sometimes another leak occurs. I’ve had these same experiences but with high voltage wiring. At a high enough voltage, around 30kV or higher, the leak manifests itself as a hissing sound and a corona that appears as a bluish glow of excited ions spraying from the leak. Try to dial up the voltage and the hiss turns into a shriek.
Why do leaks occur in high voltage? I’ve found that the best way to visualize the reason is by visualizing electric fields. Electric fields exist between positive and negative charges and can be pictured as electric field lines (illustrated below on the left.) The denser the electric field lines, the stronger the electric field.
Weak and strong electric fields
Ionization in electric fields
The stronger electric fields are where ionization of the air occurs. As illustrated in the “collision” example on the right above, ionization can happen by a negatively charged electron leaving the electrically conductive surface, which can be a wire or a part of the device, and colliding with a nearby neutral atom turning it into an ion. The collision can result in the electron attaching to the atom, turning the atom into a negatively charged ion, or the collision can knock another electron from the atom, turning the atom into a positively charged ion. In the “stripping off” example illustrated above, the strong electric field can affect things more directly by stripping an electron from the neutral atom, again turning it into a positive ion. And there are other effects as well such as electron avalanches and the photoelectric effect.
In either case, we wanted to keep those electrons in the electrically conductive wires or other surfaces and their loss constitutes a leak in a very real way.
The handheld screw driver is a wonderful tool. We’re often tempted to reach for its beefier replacement, the power drill/driver. But the manually operated screw driver has an extremely direct feedback mechanism; the only person to blame when the screw strips or is over-torqued is you. This is a near-perfect tool and when you pull the right screwdriver from the stone you will truly be the ruler of the fastener universe.
A Bit of Screw Driver History:
The kind of fun you can have with really cheap bits.
In order to buy a good set of screw drivers, it is important to understand the pros and cons of the geometry behind it. With a bit of understanding, it’s possible to look at a screw driver and tell if it was built to turn screws or if it was built to sell cheap.
Screw heads were initially all slotted. This isn’t 100 percent historically accurate, but when it comes to understanding why the set at the big box store contains the drivers it does, it helps. (There were a lot of square headed screws back in the day, we still use them, but not as much.)
Believe it or not the “Robertson” screw came out before the Phillips. Robertson just hated money and didn’t want to license his patents. So it’s only now that they’re in common use again.
Flat head screws could be made with a slitting saw, hack saw, or file. The flat-head screw, at the time, was the cheapest to make and had pretty good torque transfer capabilities. It also needed hand alignment, a careful operator, and would almost certainly strip out and destroy itself when used with a power tool.
These shortcomings along with the arrival of the industrial age brought along many inventions from necessity, the most popular being the Phillips screw head. There were a lot of simultaneous invention going on, and it’s not clear who the first to invent was, or who stole what from who. However, the Philips screw let people on assembly lines turn a screw by hand or with a power tool and succeed most of the time. It had some huge downsides, for example, it would cam out really easily. This was not an original design intent, but the Phillips company said, “to hell with it!” and marketed it as a feature to prevent over-torquing anyway.
The traditional flathead and the Phillips won over pretty much everyone everywhere. Globally, there were some variations on the concept. For example, the Japanese use JST standard or Posidriv screws instead of Philips. These do not cam out and let the user destroy a screw if they desire. Which might show a cultural difference in thinking. That aside, it means that most of the screws intended for a user to turn with a screw driver are going to be flat-headed or Philips regardless of how awful flat headed screws or Philips screws are.
Sometimes you might need to use assembly sometime to reach your project objectives. Previously I’ve focused more on embedding assembly within gcc or another compiler. But just like some people want to hunt with a bow, or make bread by hand, or do many other things that are no longer absolutely necessary, some people like writing in assembly language.
In the old days of DOS, it was fairly easy to write in assembly language. Good thing, because on the restricted resources available on those machines it might have been the only way to get things to fit. These days, under Windows or Linux or even on a Raspberry Pi, it is hard to get oriented on how to get an assembly language off the ground.
Einstein referred to her as the most important woman in the history of mathematics. Her theorem has been recognized as “one of the most important mathematical theorems ever proved in guiding the development of modern physics.” Yet many people haven’t the slightest clue of who this woman was, or what she did that was so significant to our understanding of how our world works. If you count yourself as one of those who have never heard of Emmy Noether and wish to enlighten yourself, please read on. I can only hope I do her memory justice. Not just by telling you who she was, but by also giving you an understanding of how her insight led to the coming together of symmetry and quantum theory, pointing academia’s arrow toward quantum electrodynamics.
Being a female in Germany in the late 1800s was not easy. She wasn’t allowed to register for math classes. Fortunately, her father happened to be a math professor, which allowed her to sit in on many of his classes. She took one of his final exams in 1904 and did so well that she was granted a bachelors degree. This allowed her to “officially” register in a math graduate program. Three years later, she earned one of the first PhD’s given to a woman in Germany. She was just 25 years old.
1907 was a very exciting time in theoretical physics, as scientists were hot on the heels of figuring out how light and atoms interact with each other. Emmy wanted in on the fun, but being a woman made this difficult. She wasn’t allowed to hold a teaching position, so she worked as an unpaid assistant, surviving on a small inheritance and under-the-table money that she earned sitting in for male professors when they were unable to teach. She was still able to do what professors are supposed to do, however – write papers. In 1916, she would pen the theorem that would have her rubbing shoulders with the other physics and mathematical giants of the era.
Noether’s Theorem – The Basics
Emmy Noether’s Theorem seems simple on the onset, but holds a fundamental truth that explains the fabric of our reality. It goes something like this:
For every symmetry, there is a corresponding conservation law.
We all have heard of laws such as Newton’s first law of motion, which is about the conservation of momentum. And the first law of thermodynamics, which is about the conservation of energy. Noether’s theorem tells us that there must be some type of symmetry that is related to these conservation laws. Before we get into the meaning, we must first understand a little known subject called The Principle of Least Action.
The Universe is Lazy
I would wager a few Raspberry Pi Zeros that many of you already have an intuitive grasp of this principle, even if you’ve never heard of it before now. The principle of least action basically says that the universe has figured out the easiest way possible to get something done. Mathematically, it’s the sum over time of kinetic energy minus potential energy as the action occurs. Let us imagine that you’re trying to program an STM32 Discovery eval board in GCC. After about the 6,000th try, you toss the POS across the room and grab your trusty Uno. The graph depicts the STM32 moving through time and space.
The green points represent particular points of how how high the STM32 is at a given point in time. Note that there are no values for height and time – this example is meant to explain a principle. We can say that at these points (and all points along the curve), the SMT32 has both kinetic and potential energies. Let us call the kinetic energy (kt) and the potential energy (pt). The ‘t‘ subscript is for time, as both the energies are functions of time. The action for each point will be called s, and can be calculated as:
However, action is the total sum of the difference of energies at each point between t1 and t2. If you’ve read my integral post, you will know that we need to integrate in order to calculate the total action.
Now before you get your jumper wires in a bunch, all that is saying is that we’re taking the difference in potential (p) and kinetic (k) energies at each point along the curve between t1 and t2, and we’re adding them together. The elongated S symbol means a sum, and the (dt) means as it changes over time. The path that the STM32 will take will be the path where the action S is at its minimum value. Check out the video in the source section below if you’re confused. It’s only 10 minutes and goes into this concept in easy to follow details.
Noether’s Theorem – The Details
Noether’s theorem is based upon a mathematical proof. It’s not a theory. Her proof can be applied to physics to develop theories, however. Now that we know what the principle of least action is, we can do just this.
Any law of nature can be traced back to a symmetry and the least action principle. Let’s consider two very simple examples – Newton’s first law of motion and the first law of thermodynamics.
Conservation of Momentum
Space has what is known as translational symmetry. That’s just fancy-pants talk for saying that what you do in one point in space is the same as what you do in another point in space. It doesn’t matter what hacker space you throw your STM32, it will act the same at all hacker spaces on earth. Space itself provides the symmetry. And because the principle of least action applies, you have a natural law – the first law of motion.
Conservation of Energy
Time has the same translational symmetry as space does. If I toss the STM32 now, and toss it tomorrow, it will act the same. It doesn’t matter what point in time I toss it, the results will always be the same. Thus energy is conserved between different points in time. Time is our symmetry, and the 1st law of thermodynamics is the result.
Now, I realize these examples might seem a bit useless. But when you dig a bit deeper, things get interesting. Electrical charge is also conserved. Noether says there must then be some type of symmetry involved. What do you suppose that symmetry might be? Keep following that rabbit hole, and you’ll end up face to face with QED. We’ll get there in a future article, so for now just keep Noether’s Theorem in mind.
Sources
Physics Helps, The principle of least action, video link.
Ransom Stephens, Ph.D., Emmy Noether and The Fabric of Reality, video link
2016 is the year of the consumer 3D printer. Yes, the hype over 3D printing has died down since 2012. There were too many 3D printers at Maker Faire three years ago. Nevertheless, sales of 3D printers have never been stronger, the industry is growing, and the low-end machines are getting very, very good.
Printers are also getting cheap. At CES last January, Monoprice, the same company you buy Ethernet and HDMI cables from, introduced a line of 3D printers that would be released this year. While the $300 resin-based printer has been canned, Monoprice has released their MP Select Mini 3D printer for $200. This printer appeared on Monoprice late last month.
My curiosity was worth more than $200, so Hackaday readers get a review of the MP Select Mini 3D printer. The bottom line? There are some problems with this printer, but nothing that wouldn’t be found in printers that cost three times as much. This is a game-changing machine, and proof 2016 is the year of the entry-level consumer 3D printer.
As buzzwords go, the “Internet of Things” is pretty clever, and at the same time pretty loathsome, and both for the same reason. “IoT” can mean basically anything, so it’s a big-tent, inclusive trend. Every company, from Mattel to Fiat Chrysler, needs an IoT business strategy these days. But at the same time, “IoT” is vacuous — a name that applies to everything fails to clarify anything.
That’s a problem because “IoT Security” is everywhere in the news these days. Above and beyond the buzz, there are some truly good-hearted security professionals who are making valiant attempts to prevent what they see as a repeat of 1990s PC security fiascos. And I applaud them.
But I’m going to claim that a one-size-fits-all “IoT Security” policy is doomed to failure. OK, that’s a straw-man argument; any one-size-fits-all security policy is bound for the scrap heap. More seriously, I think that the term “IoT” is doing more harm than good by lumping entirely different devices and different connection modes together, and creating an implicit suggestion that they can all be treated similarly. “Internet of Things Security” is a thing, but the problem is that it’s everything, and that means that it’s useful for nothing.
What’s wrong with the phrase “Internet of Things” from a security perspective? Only two words: “Internet” and “Things”.
I would wager a few Raspberry Pi Zeros that many of you already have an intuitive grasp of this principle, even if you’ve never heard of it before now. The principle of least action basically says that the universe has figured out the easiest way possible to get something done. Mathematically, it’s the sum over time of kinetic energy minus potential energy as the action occurs. Let us imagine that you’re trying to program an STM32 Discovery eval board in GCC. After about the 6,000th try, you toss the POS across the room and grab your trusty Uno. The graph depicts the STM32 moving through time and space.
Noether’s theorem is based upon a mathematical proof. It’s not a theory. Her proof can be applied to physics to develop theories, however. Now that we know what the principle of least action is, we can do just this.
