In essence ...

Jean-Baptiste Joseph Fourier

Joseph Fourier is one of my heroes as virtually everything one sees, hears or feels in system is due to this man's genius in creating the Fourier Transform, something, IMHO, as important as the two relativity theories of Einstein or the discovery of Quantum Mechanics in 1900.

The Fourier transform relates the time domain, in red, with a function
in the domain of the frequency, in blue. The component frequencies,
extended for the whole frequency spectrum,
are shown as peaks in the domain of the frequency.

Here is what it does to a C Major Chord

The Fourier transform applied to the waveform of a C major piano chord (with logarithmic horizontal (frequency) axis). The first three peaks on the left correspond to the fundamental frequencies of the chord (C, E, G). The remaining smaller peaks are higher-frequency overtones of the fundamental pitches.

In English ... :)

The Fourier transform breaks a function down into wavelike building blocks.

Sierra Boucher; Samuel Velasco/Quanta Magazine

As we listen to a piece of music, our ears perform a calculation. The high-pitched flutter of the flute, the middle tones of the violin, and the low hum of the double bass fill the air with pressure waves of many different frequencies. When the combined sound wave descends through the ear canal and into the spiral-shaped cochlea, hairs of different lengths resonate to the different pitches, separating the messy signal into buckets of elemental sounds.

In the early 1800s, the French mathematician Jean-Baptiste Joseph Fourier discovered a way to take any function and decompose it into a set of fundamental waves, or frequencies. Add these constituent frequencies back together, and you’ll get your original function. The technique, today called the Fourier transform, allowed the mathematician — previously an ardent proponent of the French revolution — to spur a mathematical revolution as well.

Out of the Fourier transform grew an entire field of mathematics, called harmonic analysis, which studies the components of functions. Soon enough, mathematicians began to discover deep connections between harmonic analysis and other areas of math and physics, from number theory to differential equations to quantum mechanics. You can also find the Fourier transform at work in your computer, allowing you to compress files, enhance audio signals and more.

A final word. 

It has been used to study the tides, to detect gravitational waves, and to develop radar and magnetic resonance imaging. It allows us to reduce noise in busy audio files, and to compress and store all sorts of data. In quantum mechanics — the physics of the very small — it even provides the mathematical foundation for the uncertainty principle, which says that it’s impossible to know the precise position and momentum of a particle at the same time. You can write down a function that describes a particle’s possible positions; the Fourier transform of that function will describe the particle’s possible momenta. When your function can tell you where a particle will be located with high probability — represented by a sharp peak in the graph of the function — the Fourier transform will be very spread out. It will be impossible to determine what the particle’s momentum should be. The opposite is also true.

In essence, the FT replicates reality when expressed by every digital system in the entire world. - Robert E. 

The Tides ...

(Lord Kelvin) William Thomson's first tide-predicting machine, 1876.
Built by A. Légé & Co., 20 Cross Street, Hatton

Tide-predicting machine designed by William Thomson (later Lord Kelvin), built by A. Légé & Co., 20 Cross Street, Hatton Gardens, London, 1872. The machine is a mechanical analogue computer which traces the tidal curve for a given location, by combining ten astronomical components. It is the first working machine of Thomson’s design, based on his application of harmonic analysis to tidal phenomena.

Knowledge of the tides is valuable not only for navigators, but also engineers building coastal structures, and fishermen working in shallow waters. Since tides are affected by many astronomical cycles with differing periods, predicting them is mathematically complex. William Thomson had applied the technique of harmonic analysis to tides and, in conjunction with the instrument-maker Alexander Légé, designed this mechanical computer to predict the tide curves for any given location.

As stated in the Science Museum Group's article, predicting the tides is rather crucial as civilization needs to know the extent of the rise and fall of the twice-daily movement of tides in order to successfully cope with this crucial aspect of the ocean, a process, prior to Lord Kelvin's invention of the modern analog computer in 1876, given to ad-hoc guesstimates for as long as humans have resided on planet earth. With the advent of digital, analog systems, like Kelvin's, withered away but no longer as AI needs to handle the vagaries of the real world in real-time using neural nets, the analog construct AI must have in order to function. Digital can do the job but only at enormous cost in terms of efficiency and power, something becoming increasingly problematic as society moves further into the 21st century.

Polish analog computer AKAT-1, 1959.

Arising from the dead.

Why digital has problems ...

GOING BACK TO the concept of dropping a ball, and my interest in finding out how far it travels during a period of time: Calculus solves that problem easily, with a differential equation—if you ignore air resistance. The proper term for this is “integrating velocity with respect to time.”

But what if you don’t ignore air resistance? The faster the ball falls, the more air resistance it encounters. But gravity remains constant, so the ball’s speed doesn’t increase at a steady rate but tails off until it reaches terminal velocity. You can express this in a differential equation too, but it adds another layer of complexity. I won’t get into the mathematical notation (I prefer to avoid the pain of it, to use Sara Achour’s memorable term), because the take-home message is all that matters. Every time you introduce another factor, the scenario gets more complicated. If there’s a crosswind, or the ball collides with other balls, or it falls down a hole to the center of the Earth, where gravity is zero—the situation can get discouragingly complicated.

MNow suppose you want to simulate the scenario using a digital computer. It’ll need a lot of data points to generate a smooth curve, and it’ll have to continually recalculate all the values for each point. Those calculations will add up, especially if multiple objects become involved. If you have billions of objects—as in a nuclear chain reaction, or synapse states in an AI engine—you’ll need a digital processor containing maybe 100 billion transistors to crunch the data at billions of cycles per second. And in each cycle, the switching operation of each transistor will generate heat. Waste heat becomes a serious issue.

Using a new-age analog chip, you just express all the factors in a differential equation and type it into Achour’s compiler, which converts the equation into machine language that the chip understands. The brute force of binary code is minimized, and so is the power consumption and the heat. The HCDC is like an efficient little helper residing secretly amid the modern hardware, and it’s chip-sized, unlike the room-sized behemoths of yesteryear.

To see why Analog's elegant and cool, click the Veritasium video below 

Remember, analog measures, digital counts. :)

"Moon, Turn The Tides... Gently, Gently Away" - Jimi Hendrix

 Luns's slowly leaving us but we won't notice her departure for a very long time.

The moon is drifting away from us.

Each year, our moon moves distinctly, inexorably farther from Earth—just a tiny bit, about an inch and a half, a nearly imperceptible change. There is no stopping this slow ebbing, no way to turn back the clock. The forces of gravity are invisible and unshakable, and no matter what we do or how we feel about them, they will keep nudging the moon along. Over many millions of years, we’ll continue to grow apart.

The moon used to be closer. When it first formed, about 4.5 billion years ago, molded out of rocky debris that had been floating around Earth, the moon orbited 10 times nearer to the planet than it does today. The debris, scientists believe, had come from a collision between Earth and a mysterious Mars-sized object. Fresh out of the cosmic oven, the moon was hot and molten, glowing red in the night sky. Back then, scientists say, the moon was moving away at a rate of about eight inches per year.

Our planet and its moon were always going to grow apart like this. The gravity of moons, small as they are in comparison, can still tug at their planets, causing the larger worlds to bulge outward a little bit. On an ocean-covered planet like ours, the effect shows up in the shifting tides. The moon pulls at our oceans, but those oceans pull back, making the moon speed up in its orbit. And “if you speed up while orbiting Earth, you are escaping Earth more successfully, so you orbit from a farther distance,” James O’Donoghue, a planetary scientist at JAXA, Japan’s space agency, explained to me. Scientists refer to this phenomenon as “lunar retreat”—a delightful term, as I’d prefer to imagine the moon enjoying itself at a relaxing getaway, bending its rocky body into various yoga poses, rather than slowly ghosting Earth.

"Moon, Turn The Tides... Gently, Gently Away" - Jimi Hendrix: Electric Ladyland

3 Times greater ...

2050 portends a world radically different from the one we see now based on new projections of the extent of water level rise never thought possible until now. The NYTimes Vietnam image, in particular, simply stuns yours truly given just how intense GW will become as man movers further into the 21st century.

Rising seas could affect three times more people by 2050 than previously thought, according to new research, threatening to all but erase some of the world’s great coastal cities.

The authors of a paper published Tuesday developed a more accurate way of calculating land elevation based on satellite readings, a standard way of estimating the effects of sea level rise over large areas, and found that the previous numbers were far too optimistic. The new research shows that some 150 million people are now living on land that will be below the high-tide line by midcentury.

We are so screwed.

Bangkok & Alexandra goes away as well.

Warms the cockles of one's heart doesn't it.

3 Times greater, indeed.

Addendum ...

The US also gets hit.

Miami Beach in 2050

By 2050, sea-level rise will push average annual coastal floods higher than land now home to 300 million people, according to a study published in Nature Communications. High tides could permanently rise above land occupied by over 150 million people, including 30 million in China. Without advanced coastal defense and planning, populations in these areas may face permanent flooding within 30 years.

Miami Beach/2050 - Vertical view

New Orleans, like southern Vietnam, is basically gone. 

Any questions?

Acadian Driftwood

To yours truly, Acadian Driftwood by The Band, is the best piece they ever wrote, commemorating the Acadian Deportation, an act of cruelty perpetrated by the British Empire beginning in 1755.

Soldiers rounding up terrified civilians, expelling them from their land, burning their homes and crops ‒ it sounds like a 20th century nightmare in one of the world's trouble spots, but it describes a scene from Canada's early history, the Deportation of the Acadians.

The Acadians had lived on Nova Scotia’s territory since the founding of Port-Royal in 1604. They established a small, vibrant colony around the Bay of Fundy, building dykes to tame the high tides and to irrigate the rich fields of hay. Largely ignored by France, the Acadians grew independent minded. With their friends and allies the Mi' kmaq, they felt secure, even when sovereignty over their land passed to Britain after 1713 (see Treaty of Utrecht).

Between 1755 and 1763, approximately 10,000 Acadians were deported. They were shipped to many points around the Atlantic. Large numbers were landed in the English colonies, others in France or the Caribbean. Thousands died of disease or starvation in the squalid conditions on board ship. To make matters worse, the inhabitants of the English colonies, who had not been informed of the imminent arrival of disease-ridden refugees, were furious. Many Acadians were forced, like the legendary Evangeline of Longfellow's poem, to wander interminably in search of loved ones or a home.

The sad thing about this was ...

The expulsion proved to have been as unnecessary on military grounds as it was later judged inhumane. Lawrence's lack of imagination played as big a part as greed, confusion, misunderstanding, and fear.

The Band