Tesla and 3, 6, 9

The teaching

As the record of what Tesla built and wrote teaches it.

Alternating current

A direct current flows one way, as from a battery. An alternating current reverses its direction many times a second, fifty times in Britain and Europe and sixty in North America. Its great advantage is the transformer: two coils on one iron core, which raise or lower the voltage of an alternating current with very little loss. The power lost as heat in a line grows with the square of the current, so electricity is sent across country at very high voltage and small current and stepped down near the homes that use it. The system that grew from this, with Tesla's motor at its heart, is still the one in use.

The rotating field

Tesla's own account in My Inventions tells how the key idea came. Walking in a park in Budapest at sunset and reciting Goethe's Faust, he saw the solution in a flash and drew its diagrams in the sand with a stick. The idea was a magnetic field that turns. Set coils around a ring and feed them with alternating currents out of step with one another, each reaching its peak a little after the last, and the combined field sweeps round the ring like the beam of a lighthouse.

Inside the ring sits a rotor of iron and copper. The turning field induces currents in it, and the field pushes on those currents, so the rotor turns, always a little slower than the field it chases. There are no sliding contacts to wear out, as he noted with delight when he first saw it run. This induction motor drives a great share of the pumps, fans and machines in the world.

Many currents out of step

Tesla's patents describe a system of two or more alternating currents out of step, now called polyphase. The grids of the present day use three, each a third of a cycle behind the next. Three wires carry power that separate circuits would need twice as many wires to carry, and three phases turn a motor without help. If any number belongs with Tesla's name, it is this three, the three phases of the mains.

Resonance and the coil

Every system that can swing has a natural frequency, a rate at which it likes to oscillate, like a child's swing. Pushed in time with that rate, even gentle pushes build a great motion; pushed out of time, they cancel. This is resonance, and it is the real subject of much of Tesla's work.

The Tesla coil uses it. A first circuit, with a capacitor and a spark gap, rings at a chosen frequency, and a tall second coil tuned to the same frequency takes up the energy swing by swing until its voltage reaches hundreds of thousands or millions of volts, enough to throw long sparks into the air. Its currents alternate hundreds of thousands of times a second. Such coils can burn the skin and stop a heart, and they are left to people trained to build and run them.

Power without wires

Tesla's great unfinished plan was to send power and messages around the world without wires, using the Earth itself as part of the circuit. At Colorado Springs he believed he had found that the Earth could be set ringing like a bell at its own electrical frequency, and a great tower on Long Island was to be the transmitter that did it.

The physics as it stands is this. Power passes without wires over short distances by induction, as it does into a phone resting on a charging pad, and over a few metres by tuned coils at lower efficiency. Radio carries messages anywhere, but spreads its energy so widely that only the faintest trace reaches any one receiver, enough for a signal and far too little for power. Sending usable power around the world through the Earth has never been made to work.

Building in the mind

Tesla's method of invention is the part of his work nearest to the hidden arts, and he describes it himself. He did not rush into building. When an idea came, he built it up in his imagination, changed its construction, made improvements and ran the device in his mind, even noting when it was out of balance; only when he could find no fault did he make it in metal. He held that this was possible because engineering is exact, and almost every effect can be calculated beforehand from known principles.

The automaton

In the same book Tesla gives his view of the mind, and it is the opposite of a mystic's. Tracing every image that came to him back to some earlier sight, he became convinced that each of his thoughts was prompted by an impression from outside, and concluded that he was merely an automaton endowed with power of movement, responding to the stimuli of the senses. He held that all people are such machines, moved by outside forces and mistaking the result for free will, and he built a boat steered by radio on the same principle.

Energy, frequency and vibration

A saying that travels under Tesla's name tells the reader to think in terms of energy, frequency and vibration in order to find the secrets of the universe. Its modern teachers use it to say that everything is vibration, that each thought and feeling has its own frequency, and that a person who raises their vibration draws matching things to them.

In physics the three words are exact. Energy is the capacity to do work, measured in joules. Frequency is the number of cycles in a second, measured in hertz. A vibration is a motion that repeats. Quantum theory does tie energy to frequency for every particle, through Planck's constant, and in that sense everything has a frequency; but the frequency that belongs to a resting human body by this rule is a number some fifty digits long, the same for a happy person as for a sad one of the same weight. No instrument has found a frequency belonging to a thought or a feeling. The brain's rhythms have frequencies, from a few to a few dozen cycles a second, and they are the rise and fall of currents inside the head.

3, 6 and 9 as vortex mathematics teaches

The second saying credits Tesla with holding that whoever knew the magnificence of 3, 6 and 9 would have a key to the universe, and Marko Rodin's vortex mathematics builds a system on it. Double a number again and again, 1, 2, 4, 8, 16, 32, 64, and reduce each result to a single digit by adding its digits, and the sequence runs 1, 2, 4, 8, 7, 5, then repeats for ever. Set the nine digits round a circle and join them in that order, and the path draws a looping figure that never touches 3, 6 or 9.

Its teachers read the loop as the path that energy takes through matter, the three numbers outside it as a higher dimension or the spirit of the system, and the whole as a key to physics from which new coils and boundless energy can be made.

Why the numbers behave so

The arithmetic is true, and it has a plain cause. Adding a number's digits until one digit is left gives the remainder after dividing by nine, with nine standing for no remainder, and it works because ten is one more than nine. Doubling a number that is not a multiple of three never gives a multiple of three, so 3, 6 and 9 can never enter the doubling loop; and 3, 6 and 9 double only among themselves, 3 to 6, 6 to 12 and so back to 3, and 9 to 9.

Count in another base and the pattern changes with it. Counting in twelves, adding digits gives the remainder after dividing by eleven, and doubling then visits every other remainder in turn, 1, 2, 4, 8, 5, 10, 9, 7, 3, 6 and back to 1, with only eleven, the counterpart of nine, standing apart. The special place of 3, 6 and 9 belongs to the habit of counting in tens, which came from our ten fingers, not to the structure of the universe.

Free energy

A last claim gives Tesla a lost machine that drew unlimited energy from nothing, suppressed by those who sold power. The law of the conservation of energy, tested in every branch of physics, says that energy is never made from nothing: a machine gives out at most what it takes in. Tesla's own patent on radiant energy described something lawful, a device to collect energy arriving from outside, from the Sun and other sources, much as a solar panel does today.