Paul G. Harlen

Paul G. Harlen

I am a Pittsburgh resident, Educator, Mathematician, Outdoors Lover, and Power Learner. At any given time, I could be researching any number of things just for fun, ranging from music and sports to religion and wild edibles. There is very little I know nothing about, and when I find something new to know nothing about, the research begins.

I live in Pittsburgh and love it and the city itself.
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  • How to Pass College Math Classes
    High School mathematics is much easier than college, and you might need a few tips and pointers to get your math skills up in college from a High School teacher and Mathematics Major.
  • Selling Musical Instruments: How to Get Your Money Back
    Selling an instrument can be painful, but knowing a few simple tips will differentiate your instrument from the rest and help you get the most from your sale.
  • The Bees Next Door: Is Urban Beekeeping Safe?
    Don't be afraid of the bees next door. Having a buzzing hive only 20 feet from your bedroom takes some getting used to, but it is very safe and helpful to have.
  • Styles of Banjo Design
    The Banjo sound has been made into many shapes, from tiny ukuleles to the banjo bass. Choose the right banjo for your style and sound and have a better banjo experience.
  • Folk Music: The Many Ways to Play a Banjo
    Banjos have many different styles of picking and plucking, strumming and slapping. Different Banjo styles require different strokes, literally.
  • Instrument Anatomy: The Parts of a Banjo
    The banjo is a simple instrument, but parts matter. Know your banjo anatomy so you don't spend money on things you don't need or want.
  • The American Instrument: A History of the Banjo
    The banjo is a truly American instrument. From African origins, the banjo has come to define many styles of music and has a rich history to offer interested musicians.
  • Higher Mathematics Concepts: The Goldbach Conjecture
    The Goldbach Conjecture is the prototype problem for math that is easy to disprove, hard to prove, and maybe impossible to decide.
  • Advanced Math Skills: Numerical Methods
    If you have a problem too hard to do on paper, you may need to resort to numerical methods. These approximation tricks are as old as math, but are far easier today due to computers and calculators.
  • Mathematical Mysteries: Transcendental Numbers
    Hidden between the numbers we use everyday are transcendental numbers. These numbers are hard to find, but they are actually the most numerous class of numbers we have. From pi to the exponential number e, you use them every day.
  • Saxophone Repair: Recognizing a Leaky Sax
    If your sax isn't playing right, chances are you have a leak somewhere. Leaks are problems in any woodwind, and saxophones are prone to developing tiny leaks that make for huge problems.
  • Mathematical Mysteries: Transfinite Numbers
    Transfinite numbers are bigger than infinity, or at least, some infinities. These odd numbers are actually a group of fascinating infinities, each larger than the last.
  • Saxophone Technique: The Growl
    If you want that rock and roll sound on your saxophone, knowing how to growl is key. This simple trick can add accents to your playing, helping you cut through the noise of an electric guitar without too much effort.
  • Pittsburgh Greek Food: Salonika's Gyro
    Salonika's is a popular Greek restaurant in Downtown Pittsburgh. While nothing fancy, it does have a great menu and easy, affordable options for a fast lunch or dinner.
  • Rare Musical Instruments: The Continuum
    Among the most versatile of electric instruments, the continuum fingerboard allows the musician full control of nearly every possible dimension of MIDI sound available. This is a rare, yet awesome instrument.
  • Metal and Art: Creating a Patina on Copper, Brass, or Bronze
    Your metal art might not be complete without the right patina. By pre-aging your metal, you get an antique look in minutes or hours instead of decades.
  • Rare Musical Instruments: The Keyed Bugle
    The Keyed Bugle was an antique instrument with a novel solution to the incomplete harmonic series of a regular bugle: tone holes and keys. The hybrid bugle eventually lost ground to the trumpet and valves, disappearing almost entirely.
  • Rare Musical Instruments: The Glass Armonica
    Few instruments are as haunting and ethereal as the glass armonica. Invented by Benjamin Franklin, this mechanized glass harp was a popular instrument in its day.
  • Adding Storage: Installing a New Hard Drive
    Hard disk space is cheap and easy to install into a Windows desktop. In less than half an hour, I was humming along better than ever with years worth of storage space added to my machine.
  • Home Repair Horror: My Plumbing Experience
    A simple clogged pipe became an expensive and absurd problem when I failed to really pay attention to what could (and would) go wrong.
  • Rare Musical Instruments: The Ophicleide
    The Ophicleide was an uncommon hybrid of a large saxophone and a bugle. The biggest of the outdated keyed-bugles, the ophicleide was a fascinating instrument
  • Pittsburgh History: Forbes Road and Expedition
    Forbes Avenue and his road were instrumental in taming the "frontier" of Pittsburgh. He carved a road for his military expedition that joined Pittsburgh into Pennsylvania and kicked the French from the Ohio river.
  • Pittsburgh Groceries: Wholey's Market
    Wholey's Fish Market is a full grocery store, complete with bizarre animatronic animals, a ton of ice, and a lot of cheap, quality food.
  • Pittsburgh History: The Braddock Expedition
    Before the United States existed, Pittsburgh was contested territory in the French & Indian War. Two expeditions tried to take it, and the first expedition, led by Braddock, was a disaster.
  • Rare Musical Instruments: Sopranissimo Saxophone
    The Soprillo saxophone by Benedikt Eppelsheim is technically a sopranissimo, the smallest saxophone ever made. This tiny saxophone is so small, Adolph Sax didn't even cover it in his original patent.
  • Rare Musical Instruments: The Serpent
    Before valves revolutionized brass instruments, tiny vent holes were the norm. The resulting instruments were a wonder to behold, and had some very odd shapes. The serpent is probably the strangest.
  • Saxophone Technology: Saxophone Ligatures
    The saxophone ligature helps shape your sound through removing or adding vibrations to the reed. Depending on what you want, there are plenty of options available and they won't break the bank!
  • Beginner Mouthpieces for the Saxophone
    If you are a beginner on the saxophone, don't be caught with too much or too little mouthpiece. There are many inexpensive but great mouthpieces for the new player.
  • Home Bike Repair: Cleaning a Bicycle Chain
    Eventually, you are going to have to clean the grit, grease, and grime from your bike chain. Doing so helps the chain (and your gears) last for much longer, and prevents those awful squeaks.
  • Alternative Tunings for the Mandocello
    Your mandocello can stick with the traditional tunings, or you can experiment with so many more. From new notes to easier chords, alternate tunings have many advantages and disadvantages.
  • CyberSecurity: Encrypting Your Disks or Data
    Keeping your data safe from theft is vital, and if your data is unencrypted, a thief could steal your laptop and your identity in one easy step. Encryption-at-rest is critical to your safety.
  • Invasive Wild Edibles: Japanese Knotweed
    Japanese knotweed is an invasive, horrible pest of a plant. That means that nobody will complain when you harvest some for dinner! It tastes great, and if you like rhubarb, this is another free, edible plant.
  • Pittsburgh Bridges: The Birmingham Bridge
    The Birmingham Bridge is a big, helpful mistake of a bridge in Pittsburgh, Pennsylvania. It is too big for the use, but it connects vital areas for students and residents.
  • Pittsburgh Bridges: Homestead Grays (High Level) Bridge
    The High Level Bridge, now known as the Homestead Grays Bridge, once connected Squirrel Hill to the steel mills on the waterfront. Renovated, widened, renamed, and ready to connect a new generation to Homestead's shopping and housing opportunities.
  • Pittsburgh Icons: Stephen Foster
    Stephen Foster wrote many classic American songs. Though by today's standards, they are extremely controversial, they remain in our culture due to their clever writing and aggressive rewriting of the original, quite racist lyrics.
  • Pittsburgh Instrument Shops: Hollis & Germann
    Hollis & Germann is a helpful woodwind and brass instrument shop with excellent repair technicians and knowledgeable staff.
  • Non-Western Music: Other Scales
    Not all music has the same 12 notes that we do in the U.S. Some have less, and many have more. Learning more about world music requires learning to appreciate odd scales and harmonies.
  • Math, Trigonometry, and Acoustics: Destructive Interference
    How does sound cancellation work? Why does an out-of-tune piano have a "beat" to it? Sound works in waves, and waves can add together or subtract to become bigger or disappear.
  • Using Natural Meat Tenderizing Chemicals
    Enzymes in fruit can tenderize meats more effectively than acids and impart a nicer flavor to many meats and marinades.
  • Pittsburgh Eats: India Palace
    India Palace is an affordable Indian restaurant with great access to Downtown Pittsburgh and the stadiums across the river.
  • Computation and Imagination: Turing Machines
    Turing machines are vital computers that computer scientists use to understand operations... and they don't really exist!
  • Calculus Questions: What is a Limit
    Epsilons and deltas can really confuse a simple concept. The limit is all that separates algebra from calculus, and it lets you cheat in a few, select spots dealing with infinity, zero, and the things in between.
  • Pittsburgh Shopping: Walnut Street
    If you want fashion but don't want to drive out into Pittsburgh's suburbs, Walnut Street in Shadyside is your best bet. Part mall, part boutique stores, and an easy walk to the universities.
  • Mathematical Concepts: Inductive Proofs
    Induction is a common process in mathematics which builds an infinite list out of a basic example and a proof of the "next step."
  • Pittsburgh Bars: Doubleday's Famous Burgers
    If you just want a cheap, simple burger, Doubleday's Famous Burgers is in a great location for a simple meal at a great price. It is also a great pre-game stop.
  • Science & Gastronomy: Thickening with Pectin
    Pectin is a natural thickener for many dishes, especially fruit based ones. From jelly to medicine, pectin shows up to stabilize and add texture to things we eat.
  • Rare Musical Instruments: The Hurdy Gurdy
    The hurdy gurdy is a comically named violin-bagpipe hybrid with a unique sound and a diverse heritage. One of the few truly European instruments, it has yet to catch on in the United States.
  • Woodwind Mechanics: What is an Octave (or Register) Key?
    Music, science, and a little lever action combine to make woodwinds far more versatile. By "venting" a note, register keys make instruments jump into higher octaves, and let woodwind players use more range in an instrument.
  • Classroom Mathematics Lessons: Multi-Level Classroom Games
    If you are a Math teacher, having a few games appropriate for ALL levels beats having tons of games appropriate to only one. A multi-level game offers advanced learning to students who can handle it while being fun for everyone.
  • Zoonosis and Flu Pandemics
    Zoonosis is when a disease jumps from animals to people. Many of our worst diseases and pandemics were zoonotic. Swine Flu, Avian Flu, and the Spanish Flu all jumped from animals to us.
  • Saxophone Technology: Artificial Reeds
    Cane Reeds are the standard technology for Saxophones, but other artificial reeds are making waves. Innovators continue to refine advanced artificial sax reeds with advantages (and disadvantages) over cane.
  • Ancient Technology: The Pulley
    Pulleys are hardly thought of as critical technology, until you don't have one. With just a few pulleys, you can magnify your strength enough to lift cars, and they were understood as far back as the ancient Greeks.
  • Mathematical Mysteries: Uncountable Infinity
    What is bigger than infinity? According to some math, there are even bigger infinities than the ones you might imagine. Some can be counted, and others cannot.
  • Survival Skills: Avoid Rabbit Starvation
    Rabbit starvation is a form of protein poisoning and malnutrition found in people who try to survive lean months on plentiful rabbits alone. Learning to eat diverse foods, as well as lean meat is important in survival.
  • Mathematics and Computers: Parallel Processing
    From your brain to state of the art computing, parallel processing is a completely necessary step for many complicated operations. It isn't easy to program for, but it helps to know what it means to process in parallel.
  • Pittsburgh Bridges & Tunnels: The Liberty Bridge and Tunnel
    If you live in the southern suburbs of Pittsburgh, or you need to get there, chances are you will be headed through the Liberty Bridge and Tunnel. These important crossings connect Pittsburgh to the South.
  • Woodwind Technique: Your Body as a Resonator
    You are an important part of the sound you make in a woodwind. Chances are, you shape the sound more than even your instrument does, all subconsciously until you get enough practice.
  • Musical Home Improvement: Build Your Own Practice Studio
    Creating a practice space can be affordable, and with some effort, you can insulate the inside sounds from the outside and soften the volume inside the room as well.
  • Zoology and Preservation: The Species Survival Plan Program
    Keeping threatened animals alive is tough work, and zoos are doing it every day. Find out how tough it is to run a species survival plan, and how you can help.
  • Mathematics Questions: What is an Axiom
    Axioms are at the heart of mathematics, but most people can't tell you why. This is a deep subject in math and philosophy, but most people never scratch the surface of postulates and axioms in geometry.
  • Pittsburgh History: The CIO
    The CIO, or Congress of Industrial Organizations, is now part of the AFL-CIO, but it started and achieved many great things within the city of PIttsburgh.
  • Music Theory: How to Build a Chord
    Chords get at the root of our concept of harmony. They allow single instruments or entire bands to sound harmonious, but you must be able to follow how they are made and what they mean.
  • D.C. Eats: Ollie's Trolley
    Ollie's Trolley is a treat for everyone. With a secret blend of herbs on the fries and excellent burgers for the lover of a real, classic burger.
  • Computers and Mathematics: Boolean Algebra
    George Boole invented a mathematics with just two numbers: true (1) and false (0). The simplicity of mechanizing that "boolean algebra" gave rise to computers today.
  • Pittsburgh History: The Pittsburgh Agreement
    The Pittsburgh Agreement was the equivalent of the Declaration of Independence for the Czech and Slovak peoples, and it was signed in Pittsburgh, Pennsylvania.
  • Pittsburgh History: The Lewis and Clark Launch
    Meriwether Lewis launched the keelboat that would take the Lewis and Clark Expedition up the Missouri River from right here in Pittsburgh, but this fact is almost forgotten.
  • Baritone Saxophone Questions: Low a or Low B-flat
    If you want to buy a baritone, how much is one note worth to you? This details the advantages and disadvantages of a Low A Baritone Saxophone.
  • What is the Saxello? A Soprano Sax Guide
    Soprano saxophones have more shapes than most saxes. This guide helps you know a saxello from a "baby alto" and pick the one you like most.
  • Antique Instruments: The C Melody Saxophone
    The C Melody Saxophone was a sax designed for orchestral or parlor use. Today, almost all are antiques, since they haven't been made in large numbers since the 1930s.
  • What is a Transposing Instrument?
    Many instruments in an orchestra or band are transposing instruments. While it may make them tougher to learn, it also makes them easier to play. Find out why in this article.
  • Washington D.C. Cultural Hot Spots: Ben's Chili Bowl
    Ben's Chili Bowl is more than a restaurant. It is a cultural experience highlighting the African-American experience in our nation's capital in the past fifty years. From fine arts to political upheaval, this place has seen it all
  • Survival Skills: Acorn Whistles
    Improvisation is critical for survival, and improvised signaling devices are very helpful for being rescued. An acorn whistle can be made from acorns (or anything shaped like a small cup), and can signal help for miles.
  • Saxophone Repair: Leak Lighting
    A leak light can save you a real headache when repairing your saxophone. It highlights any areas where pads may not be sealing correctly.
  • How To Make Your Own Soda
    Making your own soda pop is a fun and interesting way to play with drink flavors. Kids love it too.
  • Wild Edibles: Ginko Nuts
    Female ginko trees make a huge mess, but the nasty, smelly fruits have palatable nuts that are a food tradition in some places. Find out how to process the seeds to get rid of the stink and keep the food.
  • Music and Mathematics: Overtones
    Overtones are the difference between a tone generator and an instrument. They make instruments sound musical, and they are important to our mathematic and aesthetic study of music.
  • Technical Career Paths: Computer-Aided Drafting and Design (CADD)
    Computer-Aided Design is a great career for technical people who don't want to pursue a 4 year degree. It is fun and challenging, and requires only a couple of years of practice.
  • Ancient Technology: Vellum
    Vellum, the oldest and highest quality writing medium, is actually very fine animal skin. These thin, strong pages required effort to make, and effort to preserve today.
  • Canning Fruit Juices
    Making juice is a great way to get rid of excess fruits, and canning is a great way to store your juices for the off season.
  • Classic Baritone Saxophone Repertoire
    The least common of the "common" saxophones, finding solo music for the baritone can be tough. Look to other instruments to find music for your bari.
  • Mathematical Mysteries: The Banach-Tarski Paradox
    With six mathematically-precise cuts, can you take a ball apart and then make it into two? According to modern mathematics, you can, but according to physics, you can't. This is the Banach-Tarski Paradox.
  • Pittsburgh History: The Pittsburgh Platform
    The Pittsburgh Platform marked the breaking point between reform and orthodox Judaism. This important agreement was signed on Pittsburgh's North Side.
  • Survival Skills: Avoiding Wound Infections
    Small wounds can be fatal if they get infected. Learn to avoid infections to maximize your chance of getting out alive.
  • Preparing for College Mathematics
    The hardest classes for most people in college are math classes. Be prepared before you get to college, and learn to adjust when you get there!
  • Pittsburgh Icons: Charles Taze Russell
    The Watch Tower Bible and Tract Group was founded on Pittsburgh's North Side. This evolved into the group known today as the Jehovah's Witnesses, and are an important Pittsburgh contribution to our nation's religions.
  • Medieval Instruments: The Recorder
    The recorder isn't just a squeaky plastic instrument for kids. It was once a state of the art woodwind, and even today has a following amongst musical historians and musicians.
  • Pittsburgh Tobacco: Puffs-n-Stuff
    If you are a tobacco enthusiast, Pittsburgh serves up a real tobacconist in the form of Puffs-n-Stuff, a location for both social smoking and smoking supplies.
  • Debt Management Strategies: Roll it Over
    Personal debt can be hard to deal with. If you prioritize and plan, it gets easier and you can learn to pay off the worst bills first.
  • Chemistry of Good Food: Lecithin
    Lecithin is in nearly everything. From making your medicines work to making your chocolate smooth, lecithin is a cheap, natural emulsifier for your cooking needs.
  • Pittsburgh's Hispanic Grocer: Reyna's Foods and Taco Shack
    Reyna's is a great little Hispanic grocer and taco shack, conveniently located in Pittsburgh's Strip District.
  • Rare Musical Instruments: The Bass Saxophone
    The bass is a huge saxophone that lost almost all of its appeal by the mid-1900s. Today, the bass sax is making a comeback, and this massive sax can't help but make an impression.
  • Mulberries: The Neglected Berry
    Mulberries are a neglected berry. Subtly sweet and wildly abundant, they are an easy summer treat and almost always free.
  • Pittsburgh Traditions: The Great Pierogi Race
    Pierogis are a big part of Pittsburgh culture, and for the past 10 years, they have raced around the bases at Pirates games too. This fun tradition can't be missed.
  • Pittsburgh Groceries: Stan's Market
    If you want cheap vegetables and fruit in Pittsburgh, Stan's Market is a small, busy landmark.
  • Musical Technology: The Cane Reed
    Woodwinds in any orchestra would be useless without the humble reed. Typically, that reed is little more than a cut piece of cane, carefully treated to sound smooth and perfect.
  • Pittsburgh Groceries: Strip District Meats
    Strip District Meats gives you great prices and an old time butcher feel in the Strip District of Pittsburgh.
  • Hidden Costs of Playing an Instrument
    When picking an instrument, be careful about the hidden costs. Accessories, repairs, and consumable materials can be easily 60% of the cost of the lifetime of an instrument
  • Survival Skills: How to Dry Food
    Dehydrating food is the oldest method of preservation. Drying in the sun or over a fire will keep your food for weeks and months, and it is practical for almost any situation.
  • Advanced Mathematics and Computers: The Base 2 Number System
    Counting is the easiest thing we learn to do, but computers and mathematicians often count in odd ways to make their jobs easier. Base 2, or Binary, is the number system of computers everywhere.
  • Math and Music: Trigonometry and Sound
    Trigonometry, the study of triangles, and music are intertwined incredibly. Dig deep enough in one and you are bound to learn about the other. Why is that?
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