The Four Essentials of Science and Technology


Ignorance of science and technology rests largely on the belief that it is a vast and complicated--impossible for anyone to grasp. This belief is very destructive. The truth is that almost all scientific and technological development rests on simple tools from four areas: optics, machine tools, heat engines, and electronics!

Almost no one realizes this and those who do, either can't or won't let this be known. These four areas are discussed a little bit in the classic physics course, but since they are simple and plebian, most physics texts give less than a chapter to any of them ( and that chapter will be filled with largely useless crap).

A practical understanding of this requires almost no math and should be the birthright of everyone. Most people who know this wish to keep secret how simple it really is. "The hoi polloi are impressed by secret knowledge. Never let them know how it really is."

The saddest case occurs in the third world where the best and the brightest are sent to school to get knowledge to improve the country. They never learn what is really valuable because the curriculum throws so much junk at them. Europe and the United states achieved hegemony (and Japan and China are following) by ruthless use of these four simple areas of study. We will relinquish the secret with great reluctance.

I give you the secret knowledge here.


Optics is the first of the powerful disciplines that changed the world from ancient to modern. It began with simple magnifiers. A pretty good magnifier can be made by drilling a 1 mm hole in sheet metal and adding a drop of water which has a spherical shape. A better one can be made by grinding glass until the surface is spherical.

When two surfaces are ground or worked together until they fit perfectly at all places the result is a section of a sphere--not a rough sphere, but a near perfect one--the closest thing to perfection we have.

Grinding two glass pieces--one rotated slowly and the other moved straight across--with finer and finer grit produces two lenses one concave (bent in) and one convex (bulging out). The concave lens makes things look smaller by spreading the light rays out, and the convex lens makes them look bigger by bringing the rays together. The grit is anything harder than glass (sand, emery, silicon carbide, aluminum oxide, garnet, diamond, etc.) supplied in a graded size. Grit can be sized by screening or allowing it to settle in water (for up to a week for the finest sizes).

The lenses are used by themselves as eyeglasses or magnifiers, and are used in combination to make telescopes, microscopes, and camera lenses.

Focal length

If a convex lens is held in the sun, it will form an image of the sun at its focal length. The rays are reversable, so an image of the sun at the focal length would make an image the size of the sun at the sun's distance. We can consider anything over 10000 meters infinite, so we say rays from an infinite object converge at the focal length, and rays from the focus converge at infinity. Concave lenses don't form an image, but have a negative or virtual focal point on the back side.

Convex mirrors behave like concave lenses, and concave mirrors like convex lenses.

System sketching

The behavior of a system of lenses may be approximated by using the focal length rules to sketch rays. A point is picked on the object (usually left) side, and two or three rays traced. The first ray is the axis which goes straight through the lens with no bending. The second ray goes from the point through the focal length and emerges parallel to the axis. The third ray leaves the point parallel to the axis and passes through the focal point on the back side.

Sketching rays which aren't parallel to the axis can be made by tracing a parallel ray through the same point, and copying its bending angle to the ray to be traced.


The simplest telescope has a long focal length lens in front (the objective) and a short focal length lens in back (the eyepiece), the power or magnification of the telescope is the long focal length divided by the short and shouldn't be more than about 10 power per 25mm of lens diameter for best results.

Getting more useable power requires bigger size. The biggest are now 10 or so meters in diameter using concave objective mirrors instead of convex objective lens. The larger objective gathers more light (every doubling of diameter gives four times the light) which can be used in various instruments (usually spectroscopes--more about them later).


As the objective focal length is shortened, the telescope focusses closer and closer until it becomes a compound microscope. Microscopes were originally made as single small lenses. Single lens microscopes can be very simple, while a wide field, high magnification microscope is very complex with lots of lenses each lens correcting problems produced by the others.

Camera lenses

Cameras put the focussed image on a light sensitive material to record a picture. The image must be sharp at all points. Lenses are only sharp in the center of the image, so a lot of design work must be done to get a lens which passes lots of light and makes a sharp picture.

The simplest camera is a box with a small hole in one end rays pass through the hole and land on the sensitive material. The image is basically as sharp as the diameter of the hole. The smaller the hole the less light, so getting a good image is a compromise.

Adding a convex lens to a hole makes a sharper image. The lens and the hole (called a stop) work together. This is the start of the quest for sharper images. Designers use lots of tricks and a fair amount of math to get the sharpest image. We will look at a couple of them.

Glass bends different colors of light different amounts (this is called dispersion). The rainbow is caused by dispersion in water drops. The colors appear spread out from red to violet in an array of colors called a spectrum. By putting different materials (mostly heavy metals like lead and barium) into glass, the dispersion can be changed. By combining convex and concave lenes of different dispersion and power, the color fringes can be minimized.

The rest of the errors tend to be for off-axis points. "Bending" the lenses and adding more elements with different glasses can minimize them.


The color fringes are useful in the analysis of elements. Each element has its own "signature" of color lines which it emits when heated and absorbs from white light when cold. This is the basis of the spectroscope and spectrophotometer which are the main tools for chemistry and astronomy. The colors are spread out by a prism (glass with flat surfaces at an angle) or a grating (a surface with fine lines ruled on it which generate colors by wave interference).


Machine tools

It is possible to make spheres, cylinders, planes, and other accurate shapes by hand, using careful special techniques, but the results are very expensive. It is better to make one shape and mount it in a machine so it can be copied over and over. This is what a machine tool is. The machine tool is the foundation device for the whole industrial structure.

There are three basic machine tools in modern use: lathes, milling machines and drills. These are used for turning, threading, milling, facing, boring, drilling, and some other less common processes. Turning makes an external cylinder or rod (or a sphere, with special equipment); threading makes internal and external screw threads, milling makes complex shapes of all kinds, including gears; facing makes flat planes; boring and drilling make internal cylinders or round holes.

The ability to make these shapes is essential for nearly any technological development. Machines before machine tools were crude, expensive, and traditional. After machine tools they were common, cheap, and of incredible variety. Every part of science and technology requires some type of machining somewhere.

The machine tool is based on a flat surface and an accurate screw thread. The first flat surfaces were made by working three plate together until they fit (the surface is painted, rubbed on the other, and the high (light) points scraped down. In glass, three plates are ground and polished together until all three have flat interference lines). The first threads were made by cutting a soft cylinder with a special knife set at the angle which determined the pitch of the thread. Once the flat surface is made, it serves as a reference for the machine tools surfaces. The screw thread forms the lathe's threads by being geared to the rotating shaft (the screw turns and pushes the cutter down the rod at a regular rate, cutting the thread). Changing the gearing changes the pitch of the finished thread.

The principles of machine tools are very simple, but getting good results is often difficult. Tools bend and heat up, threads and surfaces wear, getting speeds, feeds, and angles right requires practice. The way to learn is to get access to the tools and start in building something.

Accurate measurement

Measurement at microscopic levels is done with microscopes or by contact. The simplest method is a pair of calipers set on a standard then checked against the part to be tested. If the calipers fit with very light pressure, the part is the right size. Micrometer calipers have an accurate screw thread which makes it adjustable.

Heat Engines


The simplest engine in concept ( though the most complex in practice) is the rocket engine. Hot gas is forced out a nozzle and the thrust pushes the rocket. The energy of the blast is proportional to the mass of fuel burned and the square of the velocity of the gas.

Rockets burn fuel in a confined space. The space cannot have air in it, so the fuel must supply its own oxygen. Fuels can be solid (some sort of explosive like gunpowder of ammonium nitrate and fuel oil), or liquid (like gasoline and liquid oxygen, or liquid hydrogen and liquid oxygen). Control of the solid fuel rocket is a problem since once lit, it cannot be put out or slowed down. The liquid rocket can be controlled, but requires great complexity of piping and pumps.

Stabilizing the rocket so it goes where desired is the biggest problem and usually requires a lot of computer help and sophisticated design.


The jet engine uses the nozzle of the rocket with a fan to blow air into a combustion chamber. A turbine takes some power from the exhaust to rotate the fan. This makes an engine which is extremely reliable (having very few moving parts), and very powerful. It also gets its oxygen from the air, simplifying some of the design. These engines are used in aircraft.

The difficult part is the construction of the turbine and fan. The turbine must withstand very high temperatures and so is often made of expensive titanium. The whole thing spins at high speeds, requiring very precise balancing and design.


The idea of using a spinning turbine to get power from gases isn't confined to jets. The largest engines (in electric power stations) are turbines. In these, steam from a boiler is fed into the turbine to make it spin. Though large, these engines can be extremely efficient.

Turbines have proven too expensive for most small engine applications, though some interesting work has been done.

Reciprocating engines

Reciprocating engines all have a carefully machined piston in a carefully machined cylinder. The piston is connnected by a rod to the crankshaft. As the piston is forced down the cylinder by hot gas, the motion is converted to a rotation of the crankshaft. There is ususally also a flywheel to store the force and carry the piston up on the return stroke.

The gas enters the cylinder in a number of ways. The steam engine uses a boiler to get water vapor as hot gas. The efficient stirling engine uses a variety of heated gases, including hot air. The internal combustion engine burns fuel and air in the cylinder to get the hot gas.


Electricity (whatever it is) flowing through conductors has proved the most useful of all technologies. While the number of applications of electricity seems limitless, the actual number of basic devices is small and the number of principles and formulas even smaller.

An electrical circuit or device is a battery, a relay, a motor, a generator, a transformer, a rectifier, an amplifier, a radio reciever, a radio transmitter, or a computer.


Two diffrent conductive materials in a condutive solution (acid, base or salt) make a battery. The voltage output and storage ablility of the battery is dependent on the materials used.

Batteries were the first stable source of power, making possible the discoveries which led to our modern world. the battery is the first thing determined in the design of any battery using device, since the capacity of the battery determines the usefulness of the device.


The most important discovery in electricity is that a current flowing in a wire makes a magnetic field and a wire cutting through a magnetic field makes a current flow. This one simple discovery makes possible a large number of devices and systems, including motors, generators, and relays.

A relay is a coil of wire near a soft iron plate with a switch attached. When current flows through the coil, the plate moves toward it and opens or closes the switch. Since it takes very little power to move the plate and the switch can switch huge currents, the relay is an amplifier of electricity.

Relays have lots of uses. They isolate circuits from each other, they allow a small control current to start a large machine, and they do simple computational chores like shutting something off when the temperature limit is exceeded or keeping something going after a push button switch opens.

Two interesting relay circuits use the normally open and the normally closed switch. If the normally open switch is wired around the push button, the relay stays on after the button is pushed, giving the first rudimentary computer memory. If the normally closed switch is wired in series with the relay coil, the relay will oscillate, giving a buzzer.

Motors and Generators

In a motor, a magnet of some sort (electromagnet or permanent) is mounted on a shaft and stationary coils surround it. The magnetic field is made to rotate in one set of coils (stationary or rotating) and the shaft follows the rotation.

In a simple generator, a magnet on a shaft spins near a coil. As the north pole of the magnet passes the coil, current flows one direction; as the south pole of the magnet passes the coil, it flows the other. This is the basis for the formation of alternating current or AC. Alternating current has changing current flow. the number of times the current changes direction each second is the frequency (sixty changes per second for North American power, called 60 hertz or 60 Hz).

There are essentially three types of motor or generator: direct current (DC--like battery power, no change or current direction), single phase AC (the single coil generator), and three phase AC (three different alternating waves on three different wires.

Any motor can generate power, and any generator can act as a motor. The two devices are basically interchangable. Turn the shaft of the motor and current is generated. Place current in a generator and it will spin.

There are several ways to get the magnet and the rotating field. The simplest is the "three phase induction alternating current" motor. A motor with a coil on the rotor (not hooked to anything, just shorted out), and three stationary coils will rotate with high efficiency. The shaft speed of the motor will be slower than that of the generator and the difference with generate current in the rotor coil which generates the magnetism to cause rotation.


A transformer changes the voltage and the current levels in alternating current. Two coils are magnetically coupled (through the air or a steel core). When alternating current flows through the primary coil, a changing magnetic field is created which cuts the conductors of the secondary coil and generates current in them. If the magnetic coupling is good enough, the volts per turn will be the same in both the primary and secondary. If the primary has 10 turns and 10 volts (one volt per turn), and the secondary has 150 turns, the output will be 150 volts. As the voltage raises, the current must fall since the power must remain the same. Transformers are the reason we use alternating current for power transmission. A power station generator may generate 6900 volt electricity which is transformed to 300,000 volts for cheap transmission, then transformed (eventually) to 120 volts for use in the home.


Often, it is necessary to convert alternating current to direct current. This is done with a rectifier. The rectifier is a device which acts as an electrical check valve: current can flow one way and not the other.

The rectifier outputs a series of positive or negative pulses with spaces between them. Various techniques can be used to remove the pulses and produce smooth DC, if desired.

Rectifiers have other uses as well, including demodulating radio signals, and functioning as logic gates.


An amplifier is an electronic circuit (there are thousands of different designs) that uses a small current or voltage on the input to control a larger current or voltage on the output. A PA amplifier on stage, for example, uses a microphone (a sound powered generator) producing about one thousandth of a volt as input. The output of 10 to 100 volts is fed to a speaker (a sound producing motor) and the sound exactly tracks sound input at the microphone. The power the amplifier controls comes from the wall outlet and is rectified and filtered to DC before use.

The amplifier is the big deal of electronics. Nearly every circuit is an amplifier of some sort. Digital circuits in computers are merely amplifiers which output 5 volts or zero volts with all intermediate voltages ignored. By not trying to interpret in between voltages, digital signal gain reliablility and great flexibilty, as well as being able to represent numbers to any precision. Computers need a lot of wires to do anything, however, since any single wire can't carry much information at any given time. The circuits are called digital, by the way, from the latin for finger: each wire is like holding up or putting down one finger.

The simplest amplifier circuit to work with is the operational amplifier (so called because the first ones did mathematical operations in old fashioned analog computers). It has two power inputs requiring positive and negative DC with a ground in the middle, a minus input (the output goes negative when the minus input goes positive), a plus input (ouput goes positive when the plus input goes positive), and an output. The amplifier inputs draw essentially no current, the output supplies large current, the unregulated voltage gain of the amp is essentially infinite, and a properly wired amplifier always acts to make the diffrence between the inputs zero. Various circuits are wired between the output and the minus input and between the minus input and ground to give the amplifier the desired characteristics.

The simplest amplifier example uses no special circuit at all. It is called a voltage comparator. Often these are used to compare a setpoint voltage with a real world voltage to get something done when the voltage is too high or low. In a furnace control, a setpoint voltage from a wall dial can be compared to the room voltage from a thermistor. When the thermistor is warm, the voltage is low, and the op amp output is low. When the thermistor voltage slightly exceeds the setpoint, the op amp snaps high and the furnace goes on.

In the above example, the circuit is usually stable. The op amp snaps on the the furnace goes on (though real world circuits are sometimes cranky). Stablility is the biggest problem for most control circuits. If the furnace causes the amplifier power to do something funny when it goes on, the circuit may go on and off over and over. If the microphone gets too close to the speaker, the speaker controls the microphone and the system howls or squeals.

One special type of amp makes use of controlled instability--the oscillator. This amp turns off and on over and over at a rate determined by a frequency determining network. The instability is produced by feeding a controlled amount of output back in to the input. Oscillators are essential in radio to determine the tuning frequencies, among other things.

Computers are made up of amplifiers with only two possible outputs: zero and five volts. There are three kinds: the inverter (zero output for five volts in and five volts output for zero in), the OR gate (if either of two inputs is five volts, the output is five volts), the AND gate (if both of the inputs are five volts, the output is five volts).

It is possible to state that the tool in electronics is the amplifier--one class of circuit used over and over to solve every problem.

Radio Recievers

Radio was the first darling of the electronic world. The concept is still a little startling: an alternating current of high frequency is fed into the end of a wire (the antenna), and an electromagnetic field is produced which can propagate for incredible distances. Any wire in its path can convert the field into current again. For best efficiency the wire needs to be a precisely determined length where the signal can resonate somewhat as two guitar strings do when tuned alike. The signal from the antenna is amplified, demodulated (this is done in different ways depending on the type of signal employed), and the resultant output amplified.

Light is radio energy where the length of the antenna is of atomic proportions. The frequency is astoundingly high. The early systems were very low in frequency, a little above the highest sound, and the antennas were hundreds of feet long.

The earliest radios simply turned the radio signal on and off, giving the dots and dashes (dits and dahs) of the international Morse telegraphy code. The next system changed the amplitude of the radio wave by mixing (multiplying) a sound wave with it. The resulting signal could be rectified by a diode and to yield sound (first in simple headphones, and later amplified into a speaker). The more sophisticated system changed the frequency of the transmit oscillator with the sound. While more complicated to do, the result was a little higher in quality. The first system, called continuous wave or CW, was reliable, simple and could accomodate lots of talkers in a little space. The second, amplitude modulation, or AM was the simplest way to transmit sounds and more complex data. The third, frequency modulation, or FM was more complex, but of somewhat higher quality.

There are several ways to select frequencies in recievers. Crystals can vibrate at the frequency, and electronic filters can be made. The mechanical (quartz crystal) is very stable and accurate, but cannot be changed. The electronic filters can be made with endless flexibility. Coils of wire (called "coils" or "inductors") resist the change of current through them. Metal plates held close together but not touching resist the change of voltage across them. A coil's effect becomes more powerful as the frequency raises, and a capacitor's effect becomes less. At one particular frequency, the effects become the same and either cancel each other (coil and capacitor in series) or maximize each other (coil and capacitor in parallel). Coils and capacitors can both be made variable for variable tuning of the radio.

The simplest am reciever is a tuning filter, a rectifier, an audio filter, and headphones. It uses the power of the radio station's transmitter to produce the sound. Adding amplifiers before the rectifier (radio frequency , or RF amplifiers), and amplifiers after the rectifier (audio frequency, or AF amplifiers) allow more sensitivity.

The radio filter has a wider passband as the frequency goes up. If the passband is one percent, at 100,000 hertz that's 1000 hertz--too small for quality audio. At 10,000,000 hertz, that's 100,000 hertz--enough for ten or twenty audio channels all talking at once. Solving the selectivity problem at high frequencies was essential and was done by the superheterodyne reciever.

When two frequencies are multiplied together, the sum and difference of the two frequencies are produced. Multiplying, ( also called "mixing", "heterodyning" or "modulating") the signals together gives new frequencies to work with depending on what is needed for the design.

Suppose we have the one percent passband filter, and we want the 10,000,000 hertz signal to have the band of the 100,000 hertz signal. We mix a 10,100,000 hertz signal from a local oscillator with the 10,000,000 hertz signal and get a 100,000 hertz diffrence to feed through the filter. This design gives the best of all possible worlds though it does require some care at times.

Radio Transmitters

A radio transmitter is simply an oscillator, a modulator of some kind, and an amplifier, with filters at all points, especially between the last amplifier and the antenna to lower the possibility of interference with others.


Amplifiers in computers are simple. The output of the amplifier is either zero volts or five volts (normally, though some circuits use other values). The circuits are simple--sometimes only two crossing lines formed on a silicon chip--and they do straightforward things, but the computer needs thousands or millions of these simple circuits.

The amplifiers are used to implement the three logical functions of AND, OR and NOT. The AND amplifier (called an "AND gate") gives a five volt output if all of its inputs are at five volts. The Or amplifier ("OR gate") gives a five volt output if any of its inputs is at five volts. The NOT amplifier (called an "inverter") gives five volts out if the input is at zero and zero volts out if the input is at five volts.

These three functions produce others--memory elements called "flip-flops", simple multiplication and division elements called "shift registers",counters, adders, subtractors, buffers, multiplexers,and who knows what else. These elements are then put together to form the computer. the computer has instructions (number codes) stored in memory locations pointed to by the "program counter". The basic game is to fetch the code in the program counters current location, decode it, increment the program counter, and get the next code. Jumping over code, when needed, is accomplished by loading a new number in the program counter. Programming at the number level is unbelievably tedious and error prone.

The first thing done when computers got a little bit powerful was to write programs to make programming easier. The most common form of these is the compiler.

The example compiler we will use is C++, which is very complicated, so we will look at a very tiny, but useful, part. C++ is "block oriented" meaning that all code is inside two braces ({}). Looping and jumping over is always over a whole block of code. This makes the program much more reliable than systems which allow jumping anywhere.

The heart of the compiler is formula evaluation. An algebraic formula may be entered in very nearly regular form and used for a number of purposes. Such a formula is called an expression and is made up of parentheses, variables (names of storage locations), and operators. The parentheses signal the compiler to start analyzing an expression. Expression evaluation always begins at the deepest level of parentheses and works out (this is the way parentheses work in ordinary algebra, too, if it was always confusing). There are many operators most of which are in two major classes: arithmetic and logical. Arithmetic operators work on numbers. Logical operators evaluate to TRUE or FALSE. Logical operators include equals (==), greater than (>), less than (<), ways to do AND OR and NOT, and other two valued operators. Expression evaluation is essential to almost all computing and warrants major study.

The first thing done with expressions is the assignment statement. THe expression is evaluated and the result is put in storage as in, "Temperature = 45", or "a= temp +36". In the first example, 45 is placed the the storage location called "Temperature" (which also has a numerical address which only the computer cares about), and ,in the second case, the value in storage location "temp" has 36 added to it and the result is placed in storage location "a".

The compiler also needs a way to loop over and over, a decision mechanism, and a mechanism to extend its capabilities.

Looping is done by While (){}.

Decisions are done by if (){} else {}

The capabilities of the compiler can be extended by use of the function mechanism. A function is a named block of code which can return a value that an expression can use. It can be inserted in expressions anywhere, or used as a statement by itself if it doesn't return a value.

These few simple language constructs are enough to write nearly any program. In the old days, for example, it was common to build a very tiny compiler by hand, write the code for a better one in the language of the tiny one, and so "bootstrap" the fully functional compiler. Nearly every program was written with some compiler (many of them in C++).


This simple look at technology gives a view which has never been offered. The usual exposure involves either difficult study of physics, chemistry, and mathematics, or the "gee whiz they're smart" approach of the television journalist. The material in this piece hides in the back of the physics book (some of it is unknown to the average physicist!), or in specialized publications.

These are the cornerstones of all technology. A study of physics ignores this. Educational institutions offer almost none of this for general consumption. All have missed the point.

The next piece shows the simple math which goes with this material. It is simple. You can understand it. Don't be shortchanged.