The S Curve

As far as its neighbors are concerned, a neuron can only be in one of two states: firing or not firing. This misses an important subtlety, however. A typical neuron spikes occasionally in the absence of stimulation, spikes more and more frequently as stimulation builds up, and saturates at the fastest spiking rate it can muster, beyond which increased stimulation has no effect. Rather than a logic gate, a neuron is more like a voltage-to-frequency converter. The curve of frequency as a function of voltage looks like an elongated S and it is variously known as the logistic, sigmoid, or S curve. Peruse it closely, because it’s the most important curve in the world. At first the output increases slowly with the input, so slowly it seems constant. Then it starts to change faster, then very fast, then slower and slower until it becomes almost constant again. The transfer curve of a transistor, which relates its input and output voltages, is also an S curve. So both computers and the brain are filled with S curves. But it doesn’t end there. The S curve is the shape of phase transitions of all kinds: the probability of an electron flipping its spin as a function of the applied field, the magnetization of iron, an ion channel opening in a cell, water evaporating, the inflationary expansion of the early universe, the spread of new technologies, white flight from multiethnic neighborhoods, epidemics, revolutions, and much more. The Tipping Point could equally well (if less appealingly) be entitled The S Curve. Joseph Schumpeter said that the economy evolves by cracks and leaps: S curves are the shape of creative destruction. The effect of financial gains and losses on your happiness follows an S curve, so don’t sweat the big stuff. In Hemingway’s The Sun Also Rises, when Mike Campbell is asked how he went bankrupt, he replies, “Two ways. Gradually and then suddenly.” That’s the essence of an S curve.

The S curve is not just important as a model in its own right; it’s also the jack-of-all-trades of mathematics. If you zoom in on its midsection, it approximates a straight line. Many phenomena we think of as linear are in fact S curves, because nothing can grow without limit. Because of relativity, and contra Newton, acceleration does not increase linearly with force, but follows an S curve centered at zero. If you zoom out from an S curve, it approximates a step function, with the output suddenly changing from zero to one at the threshold. So depending on the input voltages, the same curve represents the workings of a transistor in both digital computers and analog devices like amplifiers and radio tuners. The early part of an S curve is effectively an exponential, and near the saturation point it approximates exponential decay. When someone talks about exponential growth, ask yourself: How soon will it turn into an S curve? When will the population bomb peter out, Moore’s law lose steam, or the singularity fail to happen? Differentiate an S curve and you get a bell curve: slow, fast, slow becomes low, high, low. Add a succession of staggered upward and downward S curves, and you get something close to a sine wave. Children’s learning is not a steady improvement but an accumulation of S curves. So is technological change.

The Master Algorithm (2015) by Pedro Domingos

Motivational Triad

The primary purpose of your brain is to keep you alive. Our brains focus on 3 simple motivations to increase our odds of survival: avoid pain, seek pleasure and conserve energy. This is the motivational triad. You will always be motivated to do something that won’t hurt you, feels good, and is easy. This is how we humans survived back in the day. We were motivated to hunt, have sex and seek warm shelter by our desire for pleasure. We stayed alert to avoid danger. We didn’t go jogging just for the sport of it. We conserved our energy.

Powers of Ten

Powers of Ten (1977) takes us on an adventure in magnitudes. Starting at a picnic by the lakeside in Chicago, this famous film transports us to the outer edges of the universe. Every ten seconds we view the starting point from ten times farther out until our own galaxy is visible only as a speck of light among many others. Returning to Earth with breathtaking speed, we move inward- into the hand of the sleeping picnicker- with ten times more magnification every ten seconds. Our journey ends inside a proton of a carbon atom within a DNA molecule in a white blood cell.

In Motion

Angeles set in motion the sphere of fixed stars, which in turn drives all the other spheres. [France, 14th century]

A Lifestyle Brand

Has anyone written a good essay about the whole “I believe in science and trust the scientists” phenomenon which is more a lifestyle brand than an actual belief in the scientific method, which is a process, not a set of facts handed down like the Bible? Like the way science actually operates, you’re constantly trying to disprove the things we think we know. It’s not like there’s an authority and you listen to them because they’ve been handed religious truth. Scientists know this but I think at least a portion of them have enjoyed the politicization of the field and won’t point this out to the followers of the lifestyle brand version. –

The Lebenswelt

Cognitive dualism is puzzling, for it seems to be both affirming and denying the unity of reality, both affirming and denying that we human being are part of the natural order. Yet we can without contradiction accept  it, provided we recognize the explanatory priority of science. To describe the “order of nature” in terms of some complete and unified science is to give a systematic answer to the question “what exists?” But the world can be known in another way. The world known in this other way will be an “emergent” world, represented in the cognitive apparatus of the perceiver, but emerging from the physical reality, as the face emerges from the pigments on the canvas, or the melody from the sequence of pitched sounds. The relation of emergence is nonsymmetrical. The order of nature does not emerge from the Lebenswelt; its existence is presupposed by the Lebenswelt, but not vice versa.
Someone who wished to design a machine capable of delivering a Beethoven’s concerto to the ear would be helped by an analysis of the pitches and their duration. He could transcribe this analysis into a suitable digital notation and use the result to program a device capable of producing pitched sounds in sequence. The reductivist would argue that therefore the music is nothing but the sequence of pitched sounds, since if you reproduce the sequence, you reproduce the music. Sure, the music depends upon, is emergent from, the sequence of sounds. The sounds are “ontologically prior.” But to hear the music it is not enough to notice the sounds. Music is inaudible, except to those with the cognitive capacity to hear movement in musical space, orientation, tension and release, the gravitational force of the bass notes, and so on. Music is certainly part of the real world. But it is perceivable only to those who are able to conceptualize and respond to sound in ways that have no part to play in the physical science of acoustics. Again we have a useful parallel in the study of pictures. There is no way in which we could, by peering hard at the face in Botticelli’s Venus, recuperate a chemical breakdown of the pigments used to compose it. Of course, if we peer hard at the canvas and the substances smeared on it, we can reach an understanding of its chemistry. But then we are not peering at the face – not even seeing it.
I don’t want to say that I am something other than this biological organism that stands before you. This here thing is what I am. Through cognitive dualism we can grasp the idea that there can be one reality, which is understood in more than one way. In describing a sequence of sounds as a melody, I am situating the sequence in the human world: the world of our responses, intentions, and self-knowledge. I am lifting the sounds out of the physical realm, and repositioning them in the Lebenswelt, which is a world of freedom, reason and interpersonal being. But I am not describing something other than the sounds, or implying that there is something hiding behind the sounds, some inner “self” or essence that reveals itself to itself in some way inaccessible to me. I am describing what I hear in the sounds, when I respond to them as music. I situate the human organism in the Lebenswelt; and in doing so I use another language, and with other intentions, than those that apply in the biological sciences.
[The Soul of the World (2014), Roger Scruton]

Seeds of Genocide

The first step to eliminate an ethnic group, or population, is to deny that population medical treatment. In the US, several public institutions are calling for the new Coronavirus vaccine being administrate first to non-White people because White people don’t deserve it:

Harald Schmidt, an expert in ethics and health policy at the University of Pennsylvania, said that it is reasonable to put essential workers ahead of older adults, given their risks, and that they are disproportionately minorities. “Older populations are whiter, ” Dr. Schmidt said. “Society is structured in a way that enables them to live longer. Instead of giving additional health benefits to those who already had more of them, we can start to level the playing field a bit.” [NYT]

The message is clear, White people can be sacrificed and killed in a state sponsored racial, and racist, policy.

The Cambrian Explosion

The Cambrian Explosion refers to the sudden appearance in the fossil record of complex animals with mineralized skeletal remains. It may represent the most important evolutionary event in the history of life on Earth. The beginning of the explosion is generally placed about 542 million years ago, during the Cambrian Period at the start of the Palaeozoic Era. While the explosion was rapid in geological terms, it took place over millions of years – the Burgess Shale, at 505 million years old, records the tail end of the event. The explosion is particularly remarkable because all major animal body plans  appeared during this time, changing the biosphere forever. The rapid appearance of a wide variety of animals led to the development of radical new ecological interactions such as predation. Consequently, ecosystems became much more complex. The fundamental ecological structure of modern marine communities was firmly established during the Cambrian. By the end of the Period, some animals had also made the first temporary forays onto land, soon to be followed by plants. When he published On the Origin of Species in 1859, Charles Darwin puzzled over the apparently sudden appearance of complicated organisms in the fossil record at the beginning of the Cambrian Period. He noted this could be used as an argument against his controversial new theory, which predicted a more gradual appearance of simpler organisms. At the time, Darwin pointed to the imperfection of the fossil record as his only defence, arguing complex animal life must have lived long before the Cambrian, but traces of that life had not yet been found. The presence of large, soft-bodied, putative animals (problematic as they may be) in Ediacaran seas does indeed make the “explosion” appear less abrupt. But the fact remains that the Early Cambrian was a time of major change in marine animal communities and environments, with the rapid and unprecedented advent of disparate new body plans and novel ecological niches. –