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FAQs
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Why is the number 2.718 (e) so important in math and science?
In calculus there is a concept called the derivative. Basically, if you graph a curve for a mathematical formula, the derivative will tell you the slope of that graph at any given point.This is an incredibly important concept in science. It basically describes the rate of change. For example, the rate of change of distance over time is called velocity, which tells you how fast something is going. The concept of a rate of change is so important Newton invented calculus in order to figure out the other stuff he was working on. (Leibniz was working in parallel on the same thing, but for different purpose.)Well, some smart-ass named Euler decided to find if there existed a function that was it's own derivative; f (x) = df/dx as one would put it.Well, as it turned out there was. de^x /dx = e^x.What that means is that the power of e to x describes a function where it describes it's own growth.Well, as it turns out, this means that any system that has growth proportional to how much of the system you have tends to have e show up in it. Compound interest is the most common one people run into, but it shows up all the time in science as well.As for Euler?The number is named after him—Euler’s constant… abbreviated to e.
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Why are Chinese products cheaper?
In the words of Tim Cook: "The popular conception is that companies come to China because of low labor costs. I'm not sure what part of China they go to, but the truth is China stopped being the low labor cost country years ago. That is not the reason to come to China from a supply point of view, the reason is because of the skill."Let us look at the concept of labor or the involvement of labor in an every-day product. Let us compare 2 products: a plastic fork vs a plush toy. Although both products fall on opposite spectrums of the consumer life cycle (one disposable whilst the other one is reusable), both are sure to be made in China.A plastic fork is made from food-grade Polystyrene (PS) plastic pellets or beads through a process known as plastic inject molding. In here the pellets are heated in a molding machine to a viscous state and are injected into a mold. The mold produces multiple sets of forks within a matter of seconds and from there on it’s as simple as detaching the forks from a sacrificial (?) holder or tool (this is also made of PS and in most cases is recycled). From here the product is moved into packaging and then sent out of the factory for export. A fully automated machine can be set to run continuously 24 hours a day with very little monitoring by a worker, thus being a low labor product.Now, let us look at that plush toy. The stuffed animal is comprised of textile material for the cover, stuffing, two eyes and a nose. The material must be cut into pieces, sewn together and stuffed. The nose, eyes and mouth are sewn onto the material together and stuffed, requiring skilled labor(-). The cutting of the pieces may be done by hand or by machine, but the pieces are sewn together by a worker using a high-speed sewing machine. Next comes the insertion of stuffing – this is rather complex for a machine to do, as such the insertion is done by hand and the insertion point is also manually closed. It is evident that this requires much labor, therefore, this type of a product is considered a high labor product with labor contributing 70% of the total cost [1]. In the end, much like a fork, the product is moved and packaged for export.Because labor is only one part of the total cost of a product, and in many cases it's as low as 20% of the total cost, – this must indicate that there may be other factors at play in making Chinese products, such as the fork. If labor were the only factor, then most of the “plush toy/labor intensive” industries would have shifted to other countries – but only some industries already have e.g. Bangladesh, Vietnam and Mongolia to name just a few. To that extent, manufacturing of plastic forks could possibly return to the USA; but that’s not happening.Industrial production does not take place in isolation, but rather relies on networks of suppliers, component manufacturers, distributors, government agencies and customers who are all involved in the process of production through competition and cooperation. The ecosystem of doing business in China has evolved quite a lot in the last thirty years. Here are the additional factors, including labor, that affect the overall cost of manufacturing and thus make Chinese exports cheaper:A. Commendable supply chain: Supply chain activities transform natural resources, raw materials, and components into a finished product that is delivered to the end customer. No country, at present, has a supply chain more sophisticated yet flexible than China. China’s biggest advantage is their domestic availability of most of the raw materials required to manufacture a given product [2]. Not only are private entities involved in the process of outputting raw material for manufacturing. Rather, many Chinese State Owned Enterprises (SoEs) actively control and output raw materials for small factories to transform into ready-made goods. If the government is involved in such activities, it is safe to assume that this is an active industry that requires not only oversight and monitoring, but active involvement. Access to affordable raw materials helps bring down manufacturing costs to a considerable extent. As a result, having suppliers who are local to the manufacturer has gained importance as a way to cut costs[6].B. Rebate upon Export: The export tax rebate policy was initiated in 1985 by China as a way to boost the competitiveness of its exports by abolishing double taxation on exported goods[7]. China is one of over 150 countries that utilize a Value Added Tax (VAT) system. It is a tax only on the "value added" to a product, material, or service at every state of its manufacture or distribution. The VAT rate is generally 17%, or 13% for some goods. Chinese companies receive a VAT refund from the government for materials of products produced for export. Basically, factories that export do not pay any VAT on goods or raw materials used made for export – further subsidizing raw material costs. American imports to China are charged a VAT, but the U. S. doesn't have a VAT to charge Chinese imports. Moreover, Chinese manufacturers work with far lower profit margins than those in the U.S.C. Efficient Infrastructure and Logistical Access: In its fast-paced effort towards industrialization, China has built many ports (big and small), roads and railroad access. Such a system is not secluded to the big cities (Tier 1 or Tier 2 cities), it connects all of them, including Tier 4 cities or small towns used as industrial manufacturing zones. Having an efficient logistical system allows for cheaper travel costs –the cost of units (kilometers or miles) per currency (dollar or RMB) decreases. Also, an efficient infrastructure reduces overall downtime. Such is the case of India, as pointed out by Vaibhav Mandhana [3]: “Given the poor roads, a shipment from India's north can take a week or more to signNow India's south. Sometimes it is quicker and cheaper to actually get a shipment from Shenzhen than Kolkata. Time is money and all those delays add to your cost. If I could get something in two days, I could sell it immediately rather than wait two months to sell it [add up the interest costs]”"The road freight from LA to Nevada will cost you a lot more than the sea freight from China to LA."[5]D. Subsidized Utilities and Availability: Within China’s industrial areas many fixed and variable production costs are heavily subsidized. For example: electricity and water are subsidized up to 30% compared to normal household or commercial zones. Moreover, the local government gives support with land access at competitive rates, creating jobs in the area. This further helps to diminish the cost of the end product – after all you have access to cheaper land, water and light (What manufacturing does not require these? - Hell, even mining bitcoin does!). In non-industrialized or not fully industrialized countries (Indonesia, Vietnam, India), access to water and electricity remains a critical issue, until today. “In Coimbatore and other industrial places, you get power for like eight hours a day. That means the machinery lies idle for sixteen hours and that wasted capacity adds to the cost.”Do we see a trend of several factors, other than labor, which affect the overall cost of the product? Hold on, there are more!E. Bureaucracy: Barriers for entry in China, in this context, are extremely low. Although you need to fill out a huge number of papers (Customs Declaration Form, Land Annexation, Tax Filing, Compliance Related Documentation, Drawback/Rebate Forms, Annual Returns and etc.), the process is not complex. Relevant departments and accountability are there; you do not need to grease palms to get what you need; streamlined government policies are in place. Again, non-industrialized countries do not have many of these processes in place – they are in the early stages, whereas China has been through all this. I am not saying China is pure and not corrupt, there might be corruption in some cases, but the overall industrial process is so deeply rooted, that people just follow established guidelines. Greasing palms and running around places to get a stamp or a signature causes further delays (time is money) and increases overall costs. This is considered more as “Political Will” than bureaucracy; meaning the government’s will to allow you to do business is prominent thus reducing barriers for you to do business or manufacture or engage in services.F. Technology and Automation/ Skilled Labor: It would be unreasonable to discard China’s interconnectivity between technological advancement and manufacturing capacity. They work hand-in-hand. Availability of the latest technology to manufacture products of a high quality on a large scale. And let's be honest, scalability can be a very important factor in deciding price of a product. Apart from technology, China has a large population, thus having a bigger access to a wide talent pool. Availability to a greater talent pool decreases the overall demand as there is an oversupply – again, denting the costs of the product. If you recall, Tim Cook's main reason for manufacturing in China is: the depth of highly skilled labor in the manufacturing space. To rephrase what Cook said: "No other country in the world besides China has the combination of an electronic component supply chain and large pools of skilled labor needed to make iPhones on the scale which Apple needs."G. Labor: It is comparatively cheaper to many so-called “developed countries”. You can have someone do the same labor task for a comparatively lower price than say Europe or the USA for that matter. This further brings down costs. As noted before, it is not the cheapest – but it is not the most expensive either. What is important to remember here is that labor in China, is skilled – although most laborers are not trained, but have learned by doing. When you outsource to China, you’re working with time-tested factories that have been producing quality products in similar industries as yours for years on end, and in massive supply.Where a labor task might cost you $8-9 USD/hour in developed countries, it will cost you $450-500 USD for an entire month in China (8 hours a day, 28 days a month). If you do the math, that’s about $2.19 USD/hour. Countries like Indonesia a semi-skilled laborer will do it for half, $1.05 USD/hour – but the manufacturing process will be influenced by factors all the factors mentioned.H. Local Government: Local government officials are appointed, not elected. Part of their job is to help the industries and they are measured by results. Furthermore, locals compete with each other. That means Suzhou is competing with Chengdu to attract industries, and so on. Hence officials are always using their local advantages to help, attract, and grow industries, such as providing low cast land, building industrial parks, and making sure that the support infrastructure (roads, electricity, water, etc.) even local housing and schools are there. Since these officials are not elected locally, their actions are much more efficient rather than dealing a motion to go through town hall meetings or waiting for a ballot to pass for months. The downside of such efficiency could be that some environmental studies were not complete or many local concerns are not addressed fully (All credit for how to local governments operate within China go to Mr. James Yeh ).Here are few controversial factors, claimed by several sources:I. Currency: There is the ever-present theory of currency manipulation among economists, where China undervalues their currency by an estimated 30%-40%, which simply makes every product that China ships out 30-40% cheaper than those of a potential American competitor. The Yuan is manipulated and pegged undervalued to the US dollar [2]. So the price quoted in US dollars( more exports are quoted in dollars), will be cheaper than normal; (This manipulation has affected the domestic price of the product and labor wages as it has been kept much lower than it should have been. The Chinese yuan has, however, been steadily increasing in value against the dollar over the past few years.J. Compliance: The Chinese government does not bind itself with Intellectual Property issues. They allow the industry to investigate the products developed successfully elsewhere in the world. They then produce them in large quantities. Personally, there is nothing wrong in this benchmarking. Most industries do benchmark; especially in the automotive world. This saved the industry from expensive investments in R&D [4]. Although China has its own environmental protection agency, the environmental protection laws are generally lax and not enforced fully, especially at the local level. In previous years, Chinese factories cut down on waste management costs -further bringing down overall product costs. Things have been different lately, thanks to the strong efforts from the national government. Laws on IP and environmental protection are being enforced, especially after the Hangzhou G20 summit. There is still some belief that more needs to be done.If cheap labor was in itself the key driving factor, a large percentage of the labor-intensive factories would have already shifted to cheaper labor countries and lower labor-intensive jobs would have returned to the countries such as the USA - because China is not the synonym for cheap labor anymore. But that's not what we are experiencing; only certain jobs within the manufacturing field are moving to South East Asia. A huge chunk is there and is still able to reap the benefits of various factors. It will take more than a cutthroat desire for emerging economies to set up a business ecosystem that can compete with China's.Wow now over 1,000 Thanks for your upvotes! If you would be kind enough to give a like for this same article on my LinkedIn profile: https://www.linkedin.com/pulse/w...Footnotes:1. https://www.industryweek.com/env...2. https://qr.ae/TUtz1K3. https://qr.ae/TUtzTO4. https://labs.ebanx.com/en/market...5. Walter Hay's answer to How expensive is it to import to Nevada from China?6. 5 Reasons Why You Should Manufacture In China With ITI[7] China Will Continue To Dominate World Production
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What was your biggest fanboy/fangirl moment?
So, I was out with one of my friends at Starbucks. Surat, our city, had lacked this popular hangout spot since ages.. and now on 8th Aug it finally got the opportunity to witness the opening of this much awaited cafeteria.I had ordered a ‘Double Chocolate Chip Frappuccino’ since I’m only an occasional coffee drinker.. and as usual the man working there asked me my name. Me and me friend, we had decided not to give our real names, instead, say any other appropriate name..Since I’m a huge Lana Del Rey fan, I asked him to write that name for me. I had assumed that he wouldn’t know who that person is, and wouldn’t hear it correctly the first time, and would ask me how to spell it. To my surprise, HE DID KNOW IT ! He even told me, “Do you want to have Lizzie Grant/Elizabeth Grant written on the cup too?” (Lizzie/Elizabeth are the real names of Lana) and I jokingly replied, “Woah, you’re good,” and then he further asked me, “Favourite album?” And i, excited as hell, because I had finally found a person who was a Lana fan, replied, “Ultraviolence, duh!” And he (who had kind of become my best friend already) told me, “Aah, same here,” and we did a high-five!!Well, it felt like it was the best day ever, because let me tell you, Surat is the least place where I could have found a Starbucks vendor being a Lana fan.. This, this, is my biggest fangirl moment ever !! I forever long for such a situation to occur again..
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How do I read music notes?
Music is read from left to right, where going right represents moving forward in time. Since music is not capable of time-travel, it always moves forward, which means to the right. Certain symbols can tell you to go back to an earlier section of music, though, and play it again — which I guess is more like looking through a scrapbook than actual time-travel. Discuss. The grid of five lines is called the staff. Notes can be snapped to any of the lines themselves, or to any of the the four spaces between them. The higher up on the staff a note is situated, the higher its pitch relative to the rest of the staff. The the lower the note is placed on the staff, the lower its pitch. We can also extend the pitch-range of a given staff upward or downward by adding 'temporary' lines, called leger lines, above or below the staff on a note-by-note basis. You can see this has been done to the first note in the example, and it happens once again at the end of the example. Already, then, you can discern the notation well enough to tell that in the above example there is a trend in which the pitch gets higher as the music moves forward in time. If you can do that, you can read music. The rest is just filling in details, no kidding, and you simply get better with practice. Musical notation is not cryptic or arcane. Like any constructed and evolved system it has its discrepancies and idiosyncrasies, but on the whole it is quite accessible and intuitive. In the beginning, there was rhythmRhythm is sometimes neglected in the early stages of standardized music education. Because students and their teachers are so intensely concerned with making sure that the student knows where all the notes are on the instrument and where all the pitches are on the staff, sometimes rather less attention is paid to being able to understand where the notes are in time. This leads to stunted musical growth in some cases, and tragically prevents the development of many otherwise perfectly serviceable would-be funk guitarists. It is extremely important to understand that standard musical notation is not designed to tell us exactly how long the sounds last. It is only designed to tell us how long they last in relation to one another.The rhythmic values of notes, their lengths relative to one another, are in the German and American systems of nomenclature expressed as fractional relationships. Thus we have quarter notes and rests, half notes and rests, sixteenth notes and rests, and so forth. The British may have the upper hand on America in their use of the neat and logical metric system of measurements (which, you should remind them at every opportunity, they only appropriated from the French), but they must admit that they most backwardly continue the use of bizarre and uninformative names like minim, crotchet, and hemidemisemiquaver to describe these fractional relations in time-value. Though it is not at all intuitive that a semiquaver lasts one quarter the length of a crotchet, it is quite intuitive that a sixteenth note should last one-quarter the length of a quarter note: since 1/16 is 1/4 of 1/4, it takes four sixteenth notes to fill the same length of time that one quarter note fills. The Tree of Life or Holy Totem of Rhythmic Notation, then, looks something like this:one whole equals two halvesone half equals two quartersone quarter equals two eighthsone eighth equals two sixteenthsone sixteenth equals two thirtysecondsFrom this it follows that, say, four eighths equal a half, and eight eighths equal a whole. We are doing nothing more than expressing the division of time-lengths according to very basic fractional proportions which are often reducible at will to even simpler fractions. If you're brand new to reading rhythms, you may need to enlarge this diagram and study it closely — it may not 'hit you' all at once. And that's okay, as I'm sure there are still British people reading this who do not yet understand why crotchet is a very dumb name for a simple quarter note.The fraction at the left of the diagram, 4/4 (uttered as four four, not four fourths or four over four), is the time signature. In this case it tells us that there are four quarter notes, or the equivalent in duration of four quarter notes, in each measure. That is all it says. Do not let anyone (especially not anyone British) tell you that it means, "There are four quarter notes in a measure, and the quarter note gets one beat." Nothing in the time signature says the first thing about beats or who gets any of them. The top number says how many: four. No sooner than you have asked, "Four what?" the bottom number informs you: four, meaning one-fourth, representing the quarter note. So in this time signature there are four quarter notes or the equivalent in each measure. The measures, also known as bars, happen between the bar lines. Those are the vertical lines which cut through and segment the staff every so often (every four quarter notes, to be exact, in this case). Bar lines are visual references only, and have no time-value; they are not stop signs, or even yield signs.Notice that there are no quarter notes in the first measure, only one whole, and its equivalent, two halves. These two things — the whole note on top, and then the pair of half notes below — are occurring at the same time, and they occupy the same amount of time relative to one another since 1/2 x 2 = 1 (since two halves equal one whole). Since one whole also equals four quarters, hopefully you can see how the time signature works in establishing the length of a measure: though there are no quarters in the first measure, that measure still contains the equivalent of four quarters, as does every other measure pictured.Each one of these measures, then, occupies the same amount of time relative to every other measure. Though the number of notes is increasing in each measure as we move forward in time to the right, we are really just cramming more notes into the same amount of space with each passing measure: the measures are not getting longer, they are just getting busier. Those sixteen very busy-looking sixteenth notes at far right take exactly the same amount of time to go by in total as the lonesome single whole note at the beginning. You will note (terrible pun intended and in fact celebrated) that:the whole note is hollow, and has no stemthe half note is hollow, but does have a stem poking outthe quarter note is filled-in, but has no beams/flagsthe eighth note is filled-in, and has one beam/flagthe sixteenth note is filled-in, and has two beams/flagsThis is how we tell the notes apart. As the values keep getting halved going smaller in length from the sixteenth (thirty-second, sixty-fourth, etc.), we simply add one more flag each time. It takes some practice to become fluent at recognizing these values by their appearance on the page, just as it takes us time as children to learn our letters, but already you should grasp the underlying principles if I have done a half-decent job of explaining the whole thing. Sigh. A note represents a sound happening. For each of these note-values, there is a corresponding symbol called a rest. A rest is a place-holder which tells us that no sound is happening during that span of time:Each rest has a unique look, just as each kind of note does. You can see that the half rest is the whole rest turned upside-down, the quarter rest is sort of its own animal (like a crotchety Englishman, really), and the sixteenth rest is like the eighth rest only with two little doodads on it instead of one.Learning to recognize all of these different beasts quickly by sight just takes repetitious practice — it doesn't require any insightful knowledge. To see if you are grasping the basic concept of fractional/proportional rhythm and the time signature, try answering the following questions:Do six quarter notes take up more or less time than four half notes?How many eighth notes could we fit into one measure of 3/4 time?How many sixteenth notes could we fit into one measure of 6/8 time?If an incomplete bar of 4/4 time contains two eighth notes and a half rest, what one note or rest could we add that would rhythmically fill up and complete the measure? (the answers are at the bottom of this post, but don't tell anyone that.)We have not yet mentioned dotted notes. The rhythmic dot is a diabolical symbol we place just to the right of any note or rest to add half of its rhythmic value onto itself, that is, to make the dotted version 150% of the length of the un-dotted version. This means that since a quarter note is two eighth notes in length, a dotted quarter note is three eighth notes in length; since an eighth rest is two sixteenth rests in length, a dotted eighth rest is three sixteenths in length. Probably we should also mention ties. These are not the same as neckties, which I never wear if I can get away with it, since I enjoy breathing. A tie is a curved line or ligature which can join two notes together. In doing so, it combines their lengths into one sound. Therefore, the following two measures of music sound exactly the same:In the first measure there are two sounds, represented by two notes: one sound is represented by the half note and the other by the quarter. Though there are three quarter notes in the second measure, still there are only two sounds, since the first two quarters are tied together, making them sound just the same as one half note. It might not be immediately apparent why ties are needed at all; one common reason is for allowing a single sound to extend across a bar line, by tying together the notes just to either side of it.You can tie as many notes together in sequence as you wish. When an opera singer holds a high note so long that you begin to squirm in your seat, there is a pretty good chance that ties are involved somehow. Tempo, and "keeping the beat"If you are not yet dizzy and disoriented, you may be wondering how it is that musicians know how long these sounds are supposed to actually last, if the rhythmic values of the notes and rests, all these quarters and wholes and dots and ties, only describe fractional relations and not duration in terms of seconds or minutes or visits to the Department of Motor Vehicles.This is the question of tempo. If you visit Italy you'll be surprised to learn that this word can also refer to the weather, but for our purposes it means the speed of the music. We typically define tempo in terms of a steady pulse. That steady pulse can be assigned to any note value we choose. Try patting your right leg with your right hand roughly once per second, and keep that process going for a bit. It's not as important that you tick precise seconds as it is that the pulse be even and unchanging. Let's arbitrarily assign this pulse to the quarter note (in much of written music, the quarter note does get assigned the pulse, but it is by no means a rule). You are effect tapping a string of quarter notes, which looks like this:Now, while continuing to tap once per second on your right leg, take your left hand and tap your left leg twice per second, dividing each second into two even parts. For every one tap on your right leg, you will make two taps on your left leg, which also means that every other tap on the left should line up with a tap on the right. If this presents a coordination problem, you may be British. But you'll get it with a little persistence. Since a quarter note is as long as two eighth notes, you are now tapping eighth notes on the left leg while you tap quarter notes on the right leg:Try starting the process over from scratch, beginning with quarters on the right leg again and then adding equal eights, two per quarter, on the left leg — only this time, make the quarter notes go by rather faster. This means the eighth notes on the other leg will also go by faster, since they must maintain their proportion to the quarters, two to each. This is the concept of tempo applied to rhythmic notation. Feel free to let your fancy wander by speeding up and slowing down at will, but remember always to keep two eighths to each quarter.The tempo can change, and indeed any note value can be assigned to the basic pulse — quarter, eighth, whole, whatever — but the proportions of the note values, their fractional relationships to one another, do not change.We indicate general ideas about tempo using words, often dusty but beautiful old Italian words like Allegro (pretty lively), Adagio (quite slow), Presto (very fast), and so forth. We can also use a more scientific measurement called beats per minute (BPM), which is what a metronome madly ticks away at. Since we can assign the beat/pulse to any note value we want, metronome markings are generally given as "quarter note = 120 BPM," or "half note = 72 BPM," and these values are checked against the ticking of a metronome to give us the precise tempo we need. I have noticed that a common trope in dime-store theory books is to assign Italian tempo terms to ranges of BPM. Allegro might be given as 100 - 126 BPM, Andante as 72 - 88 BPM, and so on. You should know that this has no basis in reality, as these terms were invented and were in common use long before metronomes and BPM existed, and that those who claim that tempo terminology can be even approximately quantified in terms of BPM to any useful extent have been grossly misinformed. Humor me with two more brief rhythmic experiments. Define the speed of your quarter note as about once per second, as we did before (that's quarter note = 60 BMP in metronome-speak), and get it going for a bit on the right leg again, just to get your bearings. Now look at the following example:You can see that each measure of 4/4 time contains a quarter note followed by a quarter rest, twice over. Can you now 'play' this example by tapping it on your leg? Remember that the notes and rests are exactly the same length here relative to one another and to the pulse you have established — they are all quarters — and that we don't stop when we come to a bar line; bar lines are for visual reference only. If you have difficulty doing this at first, or aren't sure if you are right, try counting '1, 2, 3, 4' evenly, with each numeral representing a quarter note — just as if you are counting seconds. You should tap on 1 and 3, since that's where the notes are in each bar, and make no sound on 2 and 4, since that's where the rests are in each. Easy enough? You are now officially reading music, or at least its rhythmic aspect. Try reversing the pattern so that you rest on 1 and 3 but tap on 2 and 4 — swapping out the notes and rests — and imagine how that might look written down. For our second experiment, see if you can tap out the following:Don't fret over the new time signature (3/4). In fact, ignore it totally for the moment. Just concentrate on first establishing your quarter note pulse, and on remembering that two eighths must fit evenly into the same amount of time occupied by a quarter, relatively speaking. If we were to count this excerpt aloud, we might say:1 2 & 3 | 1 & 2 & 3You may find this slightly more difficult to do than our earlier efforts, because switching from quarters to eighths requires you to temporarily 'let go' of physically marking the pulse. In order to "keep the beat," you have to maintain an imaginary stream of even quarters in your head, just as if you were still marking them with one hand on one leg as we did at first. It is even better if you can maintain an imaginary stream of eighths in your head instead (1 & 2 & 3 & | 1 & 2 & 3 &), because this subdivision will help you internally mark the pulse with greater accuracy.This takes practice to master, particularly when the rhythms get more complicated than these. But you can do it, and you should try to master the idea very early on, because it is the heart of musicianship. PitchWe have said an awful lot about rhythm so far, because it is extremely important. But we of course also need to know how to read pitch, which tells us how high or low a note is. As we mentioned earlier, the higher the note is on the staff, the higher in pitch it is relative to the other pitches on the staff. But how do we know which pitch is A, and which is F, and which is R — wait, there is no R, as the pitches are only lettered A through G; perhaps the British have an R — how do we determine exact pitch just by looking at those lines and spaces? The answer is that the five lines and four spaces of the staff tell us nothing about pitch-letters until we place a clef on the staff. Clef is French for key, and while clefs do not at all determine 'key' in the musical sense, they are necessary for us to be able to name the pitches on the staff. The treble clef produces a series of pitches which looks like this:The first C, which is the first pitch given here, is known as middle C. The next C is pitched an octave above middle C, and the other C to the right is pitched two octaves higher than middle C. You can see that we name the pitches by counting A through G and starting over again, and that moving from one 'slot' to the next — from a space to the next line, or from a line to the next space — also moves us the distance of one letter name; none are 'skipped' when we advance one slot at a time in either direction. Try following this gamut of pitches slowly forward through time, one at a time, reciting the appropriate letter name as you come to each note. Then go backwards, that is, leftwards, and do the same thing. (Congratulations — you just broke the laws of music by time-traveling. Never do that again.)Notice that the notes can sit well below or above the staff if we temporarily extend the pattern of lines and spaces using leger lines. The bass clef produces a series which looks like this (this time we'll start at the top and descend as we move forward in time; you'll see why soon enough): Here is another crucial concept: in this example, we begin with middle C, the same pitch we began with in the treble clef, and then go down in pitch from there. That is, the first pitch in this example is exactly the same pitch, represented by the same key on the piano, for instance, as the first pitch in the previous example. This is how the treble and bass clefs are different, and yet linked. Look at the second C in this bass clef example, an octave below middle C, and imagine trying to represent that pitch using the treble clef. You'd have to draw many leger lines below the treble staff and then laboriously count them all to figure out what pitch is being represented. This is why we use different clefs (and there are others still, besides just treble and bass): because it makes the pitches on the staff easier to read depending on where we are in pitch-land at a given time. Some instruments, and all the voices, read music from a single staff and may change clefs mid-stream as needed. Still others — like the piano or the harp, which can play a very wide range of pitches — read music from two staves linked together by a bracket into a grand staff, most usually with one staff using the treble clef and the other the bass. That quite imposing structure looks and works like this:The area within the box represents the zone in which the two staves 'meet' and share exact pitches in common. Middle C is underlined as it is represented by each of the two clefs, and the D and E that follow are also pictured redundantly as they are represented by each clef. So, the C, D, and E that you see in the bass clef within the box are exactly the same pitches as the C, D, and E you see written in the treble clef within the box.As you may know, we can apply accidentals — sharps, flats, naturals, and some other even hairier critters — to these pitches in order to slightly alter them: C-sharp, E-flat, A-natural, and so forth. A sharp raises the pitch by the interval of one half-step, a flat lowers the pitch by one half-step, and a natural is most often used to cancel a sharp or flat that has just occurred somewhere earlier in the measure, so that A-sharp can be made just plain old A again, for example. Since sharps and flats require a basic understand of pitch-intervals, which is another topic entirely, I think this is a good place to stop our basic introduction to reading musical notation.This little primer is by no means comprehensive — it is not intended to be — but this should be enough of an info-dump to get you started. My hope is that you can see that the language of musical notation is actually rather simple in character, far more simple than written language, really. If it doesn't yet seem simple to you, have no fear — it takes persistent practice and study to get fluent at reading music, as with any language, but as you continue to gain fluency you will begin to see the simplicity and elegance underneath the all the symbols and their relationships to each other if you do not see it already. Remember: right = forward in time; up = higher pitch; down = lower pitch. Everything else is simply elaboration on these key bearings. Honestly, the most difficult part of reading musical notation lies in the ability to extemporaneously apply your knowledge of notation to the physical aspect of playing an instrument. That is, your understanding of musical notation isn't terribly much good until it is applied to actual music-making, which is a mental-physical behemoth all its own. When I first began reading music as a child comfortably accustomed to doing everything by ear, it was a tremendous struggle to get started. Now, about thirty years later, I can read even fairly complicated musical notation almost without conscious thought, with as little effort or less as I use to read the written word, and can hear in my mind with high accuracy the sounds represented on the page just as you can hear these words in your mind. It's just that it takes a very long time, and a lot of regular effort, to get to that point, and even now I'm not as fluent at it as I could potentially be! (And I can still play quite well by ear and can jam down at the bowling alley with the best of them. The 'wisdom' that reading music somehow harms your musicality is a nonsense notion invented by people who never bothered to learn notation very well.)Do take heart, as there are many British people who can read music. That means that you can, too. N.B.: I actually love Britain and its people, and have been there before without being arrested. Here are the answers to the rhythm questions that were asked in the section on note-values:Less time, since four halves = eight quarters, which is more than six.Six eighths could fit, since 3/4 holds the equivalent of three quarters, and one quarter is as long as two eighths, and 3 x 2 = 6.Twelve sixteenths could fit, since 6/8 implies the equivalent of six eighths, and there are two sixteenths in an eighth, and 6 x 2 = 12.A quarter. The bar of 4/4 allows for the equivalent of four quarters. The two eighth notes add up to one quarter, the half rest takes up the space of two quarters, and this adds up to the length of three quarters, leaving room for one more.J. S. Bach: from the manuscript to the Johannespassion. Just a bunch of very handsomely placed half, quarter, eighth, and sixteenth notes and rests.
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What is your opinion on the F-35?
I support the program; it’s definitely had a shaky past, including terrible management for about a decade after the contract was awarded to Lockheed, but the end result is the best bang-for-buck fighter you can get in the western world and a signNow jump in capability.There's many misconceptions about the jet (largely owing to it being the first fighter to be developed in the age of the internet) but 2 big and important ones would probably be about its cost and air-to-air combat capability:1. Cost: The F-35 cost $55.5 billion to develop, will cost about $350 billion for the United States to acquire more than 2,450 jets, and cost about $1.1 trillion to operate them (including fuel, wages, spare parts, etc) from 2010 (when the first F-35 was handed over to the US military for training purposes) to 2070 (when they're planned to retire the last F-35s). Since the program began 20 years ago, about 10% of that $1.5 trillion total figure has been spent, with all of the above costs including inflation (all figures are in cumulative then-year dollars). About $500 billion out of that $1.5 trillion is purely inflation. Source.The F-35 comes in 3 variants; the F-35A, which will make up the vast majority of the international fleet and which is designed to launch from land; the F-35B, which is for the Marines, UK, Italy, Spain and possibly others - it can hover and land vertically; the F-35C, just for the US Navy - it uses a catapult and lands on carriers with a hook like most past naval fighters. The F-35A variant as of the start of this year cost $94.6 million flyaway (flyaway = the cost of the jet; doesn't include necessary support equipment, etc) and in recent international orders to nations like Australia and Israel, has been about $200 million in program unit acquisition cost (includes US gov fees, the jet, spare parts, ground equipment, tech support, etc). By comparison, a French Rafale cost about $80m USD flyaway and $250m & $300m in PAUC in sales to India and Qatar. Kuwait paid $250 million PAUC per Super Hornet, Canada was recently quoted $300m PAUC for the Super Hornet (but with additional tech support). Kuwait paid $324m PAUC for their Eurofighter Typhoons, etc.As you can see from those numbers, the F-35 may not be cheap compared to fighters from the 70s (and in the past the F-35 was a lot more expensive), but compared to modern fighters that are in production today, it's extremely competitive in cost. The only western aircraft in production today, that I've seen repeatedly come under the cost of the F-35 is the SAAB Gripen E, and even then it only currently has 2 customers and only flew for the first time a couple of months ago.2. Combat capability: In the past, fighters favoured speed and manoeuvrability, because it was just logical - if you couldn't turn, you couldn't point your guns or radar at the enemy, or if you weren't fast, you couldn't chase down or outrun opponents. Even back then however, the best pilots (the aces that net hundreds of kills individually in WW2, etc) were the ones that learned that dogfighting was dumb when not explicitly necessary. Instead, stealth and situational awareness have proven throughout history to be even more important. From WW2 to Vietnam, some 80-90% of the aircrew shot down (based on interviews with aces and surveys of US airmen who survived shootdowns) had been clueless to the fact that they were about to be attacked.As a manifestation of this, since the 1970s / 80s, the focus on fighter technology has moved less away from increasing manoeuvrability and more towards improving sensor technology, communications systems, command and control, pilot interfaces, etc. Jets went from being able to detect enemies a few tens of miles away to being able to detect enemies a few hundred miles away. Missiles became much more intelligent and capable. Many fighters today, including the F-35, allow you to lock onto an opponent by looking at them with your helmet (even if they're at your 3'o'clock, or in the F-35's case, even if they're at your 6'o'clock) and pressing a button on your flight stick. From there, modern missiles can launch, pull a 50 to 100G turn at Mach 2 to 4 and detonate next to the enemy's plane, tearing it in half with a continuous rod warhead.In other words, being able to out-turn an enemy and get behind them with your gun, is about as important as hand-to-hand combat and bayonet drills are for modern infantry, with the past 40 years and 500 or so air-to-air kills (made around the world) being testament to that through the duopoly that all-aspect and BVR missiles have obtained:(Source)On the odd occasion, it can be useful, but more often than not, its taught primarily more to help provide core skills and traits, such as controlled aggression, physical fitness, training muscle memory and maintaining awareness while under pressure. A platoon of US soldiers aren't going to lose against a platoon of (eg) Chinese soldiers just because the latter is more capable of hand-to-hand combat.In the F-35, what they've done is taken the R&D budget and system design space, carved out enough for kinematics, so that the F-35 is still an improvement on the jets it replaces (the F-16C, F/A-18C and AV-8B primarily), but then dedicated the rest to stealth, sensors, comms, automation and human interfacing. It's been quoted by multiple sources as being stealthier than the F-22, which was previously the stealthiest aircraft in the world (at least against SHF radars). It has smaller but more advanced derivatives of the F-22's radar and passive RF sensors, as well as the world's first 360 degree staring IRST (which means that so long as they're not flying through thick clouds, no fighter can get within visual range of an F-35 undetected) and an integrated telescopic IRST / TFLIR. It has a proprietary data link which compares to Link 16 (the main data link in use today) as broadband compares to dial-up. It has advanced sensor fusion and automation that means that the jet will automatically check out contacts with untasked sensors (even on other F-35s) to gather more data and fill in blanks; it'll automatically determine whether multiple sensors are looking at the same target or if there's multiple; it'll compare IR signatures, radar signatures, radio emissions, etc against a databank to automatically identify what type of air / land / sea threat the jet is looking at, etc. It has a helmet that projects augmented reality symbology onto the visor, replacing the HUD of a conventional fighter; the helmet also projects video feeds onto the visor to give the pilot a much larger display than can be fit into a fighter cockpit; those video feeds include a stitched 'x-ray' view through their aircraft using the 360 degree staring IRST (DAS) sensors and gives them night vision at the press of a button instead of requiring bulky and battery-powered NVGs. The cockpit is also the first to use a big panoramic display that lets pilots customise their cockpit more and focus better on what they need to.What that means is that even though it's not as agile or fast as the F-22, the F-35, even with incomplete software that artificially limited the jet's manoeuvrability and payload to just 2 air-to-air missiles (and no gun), was still able to achieve a 20:1 kill ratio against F-16s and F-15s at Red Flag earlier this year (the biggest, most advanced, real-world air combat training exercise on Earth, with that Red Flag in particular being the toughest ever organised). In other exercises like US Marine Weapons and Tactics Instructor courses and US Navy Top Gun courses, F-35s have also been racking up 20:0, 24:0, etc (undefeated) kill ratios where previously F/A-18s, etc going up against the same threats would sometimes have half their jets 'shot down'. As far as air-to-air goes, the F-35 is essentially an F-22 with the Pareto principle applied to it.
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