Three-Phase Waves, Tilting Tables, and HFT Vibrations: A Thought Experiment in Currencies and Cycles :PART I – Analytics & Forecasts – 12 April 2025

Introduction
Foundations of Three-Phase Wave Theory in Electrical Engineering
Wave Phenomena in Physics: A Brief Overview
Transition to Financial Markets
The Table Thought Experiment
Einstein-Style Mind Experiments
Introducing High-Frequency Trading (HFT) Vibrations
Parallels to Real-World Market Dynamics
Deeper Implications and Interpretations
Conclusion

1. Introduction

Currency markets, electricity grids, quantum wave functions, and even the behavior of furniture (like a table balancing on one leg) might seem like disparate topics best kept in separate realms of discussion. However, imaginative thought experiments—akin to those famously utilized by Albert Einstein—can yield surprising insights when we connect ideas across different disciplines.

In this wide-ranging article, we take three key concepts:

Three-phase wave theory from electrical engineering,
Wave phenomena from classical and modern physics, and
An inventive table analogy featuring three currencies (USD, GBP, and JPY),

…to paint a picture of how cycles, balance, phase shifts, and vibrations might explain certain aspects of financial markets—especially foreign exchange (FX). We’ll also consider how the rapid-fire nature of modern high-frequency trading (HFT) could act as tiny “vibrations” that, under certain conditions, either dampen or destabilize this financial “table.”

By the end of this journey, the goal is not to present a rigorous mathematical model for forecasting exchange rates or a foolproof trading system. Rather, it is to illustrate how wave-like thinking and mind experiments open new perspectives on how and why currencies move—and what happens when the system is shocked by relentless micro-forces.

2. Foundations of Three-Phase Wave Theory in Electrical Engineering

2.1 The Rise of AC Power

In the late 19th and early 20th centuries, a monumental “War of Currents” took place between direct current (DC) systems championed by Thomas Edison and alternating current (AC) systems advanced by Nikola Tesla and George Westinghouse. AC ultimately won out on a wide scale due to its efficiency in power transmission over long distances and its ability to step voltages up or down with transformers.

Within the AC realm, engineers discovered that using three separate phases—each offset by 120 degrees—offered significant advantages for power generation and distribution. This arrangement became known as three-phase power and remains the backbone of modern electrical grids.

2.2 Three-Phase System Basics

A three-phase AC system can be visualized as follows:

Voltage waveforms:
Balanced loads: If three identical loads are connected—one on each phase—then, ideally, no net current flows through the neutral or ground wire. The vector sum of the three phase currents is zero.

2.3 Balancing and Phase Shifts

The key beauty of a three-phase system is that it can provide nearly constant power to a balanced load. In single-phase AC, power fluctuates between positive and negative peaks, while three-phase AC “smooths out” these fluctuations.

It’s this notion of summation to zero (under ideal, balanced conditions) and phase shifts of 120° that inspire our later analogy. If we view currency markets in a similar “three-phase” perspective—USD, GBP, and JPY—balanced conditions mean no net arbitrage or “tilt.” But if some mismatch occurs, you effectively get a net resultant “voltage” in one direction, analogous to a currency attracting more capital than the others.

3. Wave Phenomena in Physics: A Brief Overview

3.1 Mathematical Wave Functions

Across physics, waves can be represented mathematically in various ways, often as:

f(x,t)=Asin(kx−ωt+ϕ),f(x, t) = A \sin(k x – \omega t + \phi),f(x,t)=Asin(kx−ωt+ϕ),

where AAA is amplitude, kkk is wavenumber, ω\omegaω is angular frequency, and ϕ\phiϕ is a phase offset. In quantum mechanics, “wave functions” describe probabilities, but in a more classical sense, the wave equation captures oscillations in media (sound waves, water waves, electromagnetic waves, etc.).

3.2 Superposition and Interference

A hallmark of wave behavior is the superposition principle: when two or more waves overlap, the resulting waveform is the sum of the individual waves. This can lead to constructive interference (peaks add) or destructive interference (peaks and troughs cancel). In markets, “constructive interference” might be analogous to multiple bullish factors aligning, amplifying a price move. “Destructive interference” might occur when bullish and bearish signals negate each other, resulting in sideways or minimal net movement.

3.3 Resonance and Natural Frequencies

If a periodic force is applied at or near a system’s natural frequency, the system can start to oscillate with increasing amplitude. Think of a child pushing a swing at the right moments. This phenomenon—resonance—explains how small, periodic inputs can generate large responses. In our currency analogy, if high-frequency trading inputs land in a way that resonates with the “natural cycle” of capital flows among the three currencies, we could see outsized swings or even structural breakdown.

4. Transition to Financial Markets

4.1 Why an Analogy?

Financial markets might seem far removed from sinusoidal waves in physics or from rotating phasors in electrical engineering. Yet, the concept of cyclical or oscillatory behavior is pervasive in economics and finance:

Interest rate cycles: Central banks raise and lower rates in somewhat predictable cycles over years.
Business cycles: Economies expand and contract, influencing capital flows.
Trading cycles: Traders often speak of “market waves,” “cycles,” or “Elliott Wave patterns,” attempting to characterize crowd psychology and price momentum.

By borrowing the language of waves, we can glean fresh insights: is the market near a peak or trough? Are multiple cycles overlapping? Is there a phase shift that points to which currency will strengthen next?

4.2 Currency Markets as Oscillating Systems

Foreign exchange (FX) markets pair one currency against another. For instance:

EUR/USD indicates how many US dollars one euro can buy.
GBP/USD indicates how many US dollars one British pound can buy.
USD/JPY indicates how many Japanese yen one US dollar can buy.

If we focus on three currencies—USD, GBP, and JPY—then we get three pairs:

GBP/USD (pound-dollar),
USD/JPY (dollar-yen),
GBP/JPY (pound-yen).

Much like a three-phase power system, these three pairs interrelate. In an ideal state, there is no arbitrage: converting GBP to USD to JPY and back to GBP should yield no net profit. If a market mismatch arises, a quick triangular arbitrage might exist, similar to having an unbalanced three-phase load that creates a net current.

4.3 Triangular Relationships Among Currencies

A real or hypothetical scenario: Suppose you hold 1 GBP. You convert it to USD at the prevailing GBP/USD rate. Then you convert those USD to JPY at the USD/JPY rate. Finally, you convert those JPY back to GBP at the GBP/JPY rate. If all is balanced, you end up where you started. However, a moment of imbalance (like a slight shift in one rate relative to another) could yield a tiny profit or loss. This fleeting “excess” or “deficit” is akin to a net resultant vector in an otherwise zero-sum three-phase system.

5. The Table Thought Experiment

5.1 Setting the Stage: Three Men, One Pivot, and All the World’s Cash

Imagine a round table perched precariously on one central leg—a pivot. Around this table sit three men:

Mr. USD
Mr. GBP
Mr. JPY

Now, imagine all the money in the world—in the form of cash, coins, gold, or whatever representation you like—piled on top of this table. Although physically impossible, it’s a conceptual device. Because the table stands on a single pivot point, wherever the “weight” (cash) accumulates most heavily, the table tilts in that direction.

5.2 Rocking Motions and Money Flow

If Mr. USD persuades global investors that the dollar is a safe bet—for instance, due to rising interest rates—more and more cash is heaped in front of him. The table tilts toward his corner. If suddenly Mr. GBP makes a compelling case (e.g., strong economic data in the UK, an attractive policy shift by the Bank of England), some portion of that money slides across the table, reversing or redirecting the tilt toward GBP. Over time, the system can appear to rock back and forth based on whose corner is attracting more capital.

5.3 Comparing the Table to Three-Phase Balance

In a perfect “three-phase” scenario, the money distribution is absolutely balanced—equal weight at USD, GBP, and JPY corners. The table sits flat, showing no tilt. However, markets are rarely so neat. A slight advantage in yields, trade balances, or macroeconomic expectations can cause a tilt. That tilt may remain for a while or shift quickly if conditions change.

5.4 Balanced vs. Imbalanced Currency Distributions

Balanced: No tilt, no big opportunities for arbitrage. Symbolizes an equilibrium state.
Imbalanced: One currency corner becomes heavy-handed, either from overconfidence, safe-haven flows, or interest rate differentials. Arbitrage or corrective forces often arise, attempting to rebalance the table.

This interplay is reminiscent of wave theory, where equilibrium (zero net amplitude) can be disturbed by an external force, leading to oscillations. Eventually, friction or damping can bring the system back toward stability—unless there’s a continuous driver that perpetuates or amplifies the tilt.

6. Einstein-Style Mind Experiments

6.1 “Riding the Wave” of a Currency Pair

Albert Einstein famously imagined himself riding a beam of light to explore the implications of special relativity. In the same spirit, imagine you shrink down and stand on a GBP/USD chart as it moves up and down over time. You feel the “swell” when GBP strengthens (the line on the chart moves higher), and you feel the “drop” when GBP weakens against USD.

6.2 Rotating from USD to GBP to JPY

Next, you hop off the GBP/USD wave and onto the USD/JPY wave. Maybe you discover that USD/JPY has a different shape or phase—perhaps it’s lagging or leading the GBP/USD cycle by some fraction of a period. Finally, you shift to GBP/JPY, noticing that if GBP has been strong against USD, and USD is strong against JPY, then GBP might be extremely strong against JPY (or the inverse if all conditions reverse).

In a perfect equilibrium, you’d ride these three waves and return to your starting point with no net gain or loss. But if some mismatch arises (a misalignment of wave peaks and troughs), you might find yourself at a higher or lower “height” than you began—akin to discovering a brief triangular arbitrage.

6.3 Visualizing Arbitrage as Tilts and Shifts

The table analogy and wave riding analogy combine into a single mental image of cyclical flows of capital. Money slides around the table in waves. If everything is in sync, the net effect is balanced. If there is a timing or amplitude mismatch, it creates an opening for profit or signals an emerging trend. In a real market, these mismatches often last mere seconds or minutes, especially when heavy algorithmic trading participants stand ready to exploit them.

7. Introducing High-Frequency Trading (HFT) Vibrations

7.1 Rapid Taps on the Table: The Impact of HFT

Now, we add another layer to the thought experiment: high-frequency traders. Picture them as thousands of tiny hammers tapping around the table’s edges. Each tap is a tiny trade—often lasting microseconds or milliseconds—buying or selling currency to capture a fraction of a cent in profit.

Instead of a gentle “rock” as funds flow from one currency corner to another, you get rapid micro-impulses. The table might start to shudder or vibrate. If the table (market) has enough friction or damping (i.e., liquidity, regulation, balanced order books), these micro-taps might not do much more than cause small ripples. But if conditions align with the system’s natural frequency—or if damping is weak—these micro-taps can add up to significant oscillations.

7.2 Resonance and Damping in Financial Systems

In physics, when a small periodic force is applied repeatedly at the natural frequency of a system, resonance occurs. For a table, resonance might manifest as an extreme rocking motion or even structural failure if it’s not built to handle such amplitude.

In financial terms:

Resonance: The repeated trades match some cyclical pattern in order flows or liquidity conditions, amplifying price swings.
Damping: Market participants who provide counter-orders, regulatory measures, circuit breakers, and risk constraints can absorb or limit these swings, keeping the system from flying apart.

If HFT strategies collectively exploit the same patterns or liquidity pockets, they might inadvertently generate a resonant frequency. That can escalate volatility rapidly, sometimes culminating in a “flash crash.”

7.3 Self-Destruction or Natural Rotation?

From this point, the system can branch into two broad paths:

Self-Destruction: If the rocking grows too extreme, the table’s leg could snap (the market “breaks”). In real markets, this might look like trading halts, exchange outages, or flash crashes where liquidity disappears almost instantly.
Natural Rotation: Alternatively, if the table’s structure (market infrastructure) is robust and the impetus from HFT is moderate, the system might “learn” to rotate or spin. In that scenario, the trading taps produce a cyclical or swirling flow of capital among currencies, never fully crashing but never settling into a calm equilibrium either.

In practice, markets often do a bit of both. You might see short-lived self-destructive episodes (spikes of extreme volatility), followed by rotations or partial stability as participants adjust strategies or as circuit breakers kick in.

8. Parallels to Real-World Market Dynamics

8.1 Flash Crashes and Liquidity Vacuums

Flash crashes happen when liquidity—normally provided by market makers or HFT firms—vanishes in an instant. For instance:

May 6, 2010, the U.S. stock market plunged nearly 1,000 points in minutes.
Currency “flash crashes” have periodically occurred during low-liquidity hours, such as overnight moves in GBP or JPY.

In our table metaphor, it’s as if the support near one currency corner suddenly disappears. The pile of money slides uncontrollably, tilting the table at a dangerous angle. If no one steps in to stabilize it (place offsetting orders), the table tips so far it might effectively “collapse.” Markets usually impose circuit breakers—pauses to trading—to let participants regroup, akin to bracing the table leg so it doesn’t snap entirely.

8.2 Circuit Breakers, Damping, and Regulation

To prevent catastrophic resonance or unstoppable tilts, market operators and regulators introduce mechanisms. For example:

Circuit Breakers: If prices drop or rise too quickly, trading halts for a set period.
Orderly Trading Rules: Exchanges may reject or slow orders that are far off the current price.
Central Banks: In extreme cases, central banks might intervene in currency markets to restore confidence, akin to physically grabbing the table leg and centering it.

These forms of damping ensure that repeated tapping or sudden shifts don’t immediately shatter the system.

8.3 Cyclical Capital Flows Among Major Currencies

On a broader timescale, capital tends to rotate among major currencies for macroeconomic reasons:

When the U.S. Federal Reserve raises interest rates, funds might shift toward USD.
If the European Central Bank signals tighter policy or stronger growth prospects, the euro or pound may attract inflows.
If global risk sentiment deteriorates, the yen may strengthen as a “safe haven,” pulling funds out of USD and GBP.

These flows often take months or years to play out, forming medium- or long-term “waves” in the market. HFT plays out on microsecond timescales, yet both phenomena coexist, layered like different frequencies in a complex wave function.

9. Deeper Implications and Interpretations

9.1 Chaotic vs. Cyclical Market Behavior

Markets are famously prone to chaotic behavior—small changes in initial conditions can lead to large, unpredictable outcomes. Nonetheless, broad cycles do emerge over time: expansions, recessions, rate-hike cycles, carry-trade unwinding, etc. The table analogy suggests a quasi-cyclical rocking motion that never fully settles. If we introduced more “legs” (more currencies), the system might appear even more complex but still revolve around similar principles of distribution and rebalancing.

9.2 The Role of Psychology and Expectations

Human (and algorithmic) psychology heavily influences how money moves. Fear, greed, momentum, and narrative can create feedback loops. If market participants expect USD to strengthen, they buy USD, thus strengthening USD in a self-fulfilling prophecy until contradictory evidence emerges. In wave terms, it’s another force pushing the amplitude of a cycle until a reversal occurs. The “table tilt” might be modest at first but can accelerate if enough players shift their weight.

9.3 Possible Futures of Currency Market Structures

As technology advances:

Speed of Trading: Microsecond-level trading might push us closer to physical limitations (speed of light, data center proximity).
Automated Market Making: Could reduce flash crashes by providing continuous liquidity, akin to adding multiple stabilizing legs or hydraulic dampers under the table.
Central Bank Digital Currencies (CBDCs): Might reshape how currency transitions occur, potentially altering the “tilt dynamics” if cross-border transactions become instantaneous and frictionless.

In each scenario, we still confront the same fundamental aspect: money flows from one corner to another, and the system’s reaction depends on whether the flows are gentle and manageable or abrupt and resonant.

10. Conclusion

This expansive, imaginative tour bridges three-phase wave theory, wave phenomena in physics, and a metaphorical table with three currency “characters” (USD, GBP, and JPY) competing for a finite pool of global cash. By layering in the concept of high-frequency trading as tiny “vibrations,” we see how the system can either:

Self-destruct under extreme strain, akin to a flash crash or “snapped table leg,” or
Enter a rotating or oscillatory mode, where capital moves in waves among the currencies, never fully at rest.

Much like Einstein’s mind experiments, the purpose of this exploration is not to assert that wave equations from physics or three-phase power engineering directly control FX markets. Rather, these analogies and mental exercises help us see familiar phenomena from fresh vantage points—highlighting the roles of balance, phase shifts, resonance, and equilibrium/disequilibrium.

Ultimately, currencies, like waves, are in constant motion. They rise, fall, tilt, and shift in response to a spectrum of forces, from macroeconomic fundamentals to the micro-impulses of algorithmic trades. With imagination, we can interpret these movements as part of a grand, dynamic tapestry—a perpetual interplay between flows, balances, and vibrations.

Perhaps the key takeaway is that no currency “corner” controls the table forever. When one corner grows heavy with capital, the tilt invites eventual reversion or rotation. In essence, what appears dominant today might be overshadowed tomorrow, a cycle that continues as long as money flows and markets function.

So, whether you’re a curious observer, an FX trader, or someone enthralled by the elegance of wave analogies, remember the single-legged table and the three men—Mr. USD, Mr. GBP, and Mr. JPY—as a lens through which to view how markets sway. In that lens, tiny shifts in confidence, policy, or data can pivot the entire system, rocking or rotating the table in sometimes predictable, sometimes startling ways. And, if those moves align with a resonant frequency—beware. The wave might build into something bigger and more powerful, highlighting just how delicate and enthralling the balance of global finance can be.

A Cautionary Note to High-Frequency Traders:

Beware the table’s spin. If your relentless microsecond trades keep tilting and tipping this single-legged platform, momentum can build faster than you realize. Imagine it now: the table shifts from USD to GBP, from GBP to JPY, then back again—only this time it doesn’t settle. It starts a full rotation. That’s when you’ll find me directly opposite your position, a full 180 degrees in front of you.

Think of it as cosmic irony: the faster you “tap,” the more you risk whipping the entire market into a spin—until suddenly you’re facing someone who anticipated your every move from the other side. In that moment, your advantageous microseconds might dissolve into spiraling risk, leaving you on the wrong edge of a rapidly rotating table.

Your algorithms may exploit tiny dislocations in seconds or microseconds, but remember: those taps can resonate far beyond your intended scope. The table is finite, and its single pivot stands ready to amplify or betray you. If it starts spinning under your algorithm’s hand, be prepared: I’ll be there, exactly 180 degrees ahead, ready to meet you head-on.