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The three ways to solve Fokker-Planck equations: PDE evolution, stochastic (independent) or deterministic (coupled) particle systems.

85,288 views • 2 years ago •via X (Twitter)

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The three-body problem is a classic and notoriously difficult question in physics and mathematics. It asks: How do three objects, such as stars, planets, or moons, move under the influence of each other’s gravity? Unlike the simpler two-body problem, which has precise and predictable analytical solutions (like the Earth orbiting the Sun in an ellipse), the three-body problem quickly becomes chaotic and unpredictable. This complexity arises because each object's motion constantly affects, and is affected by, the other two. These gravitational interactions form a tangled and unstable system. In fact, there's no general formula that can solve all three-body scenarios exactly. This was first demonstrated in the 19th century by Henri Poincaré, whose work laid the foundations for chaos theory. While exact solutions remain elusive, scientists have discovered certain special cases where the motion is stable or periodic. One well-known example is the Lagrange points, where three bodies can maintain a stable triangular configuration. However, such neat solutions are rare. Today, thanks to powerful computers, researchers can simulate three-body systems with remarkable accuracy, helping us study triple-star systems, exoplanets, and asteroid dynamics. Yet even small changes in the starting conditions can lead to dramatically different outcomes, highlighting the sensitive dependence on initial conditions that defines chaotic systems. The three-body problem is actually a specific case of the broader n-body problem, where n can be any number of interacting bodies. As n increases, the complexity and unpredictability rise even further. The three-body problem serves as a vivid example of how simple laws of nature, like Newton’s law of gravity, can produce behavior that is intricate, unexpected, and profoundly difficult to predict.

Erika 

215,611 views • 1 year ago

This fact absolutely shatters evolution. ...And makes the intelligent design in Life certain. All the systems in Life that make things function - like everything that enables birds to fly - require a whole set of complex interconnected parts. Nothing works in isolation. Something evolutionists overlook is how the nature of all these systems are intricately interconnected. Every part relies on something else to make it work. You need the whole system, down to the DNA itself, or the function fails. This coordinattion between so many systems makes step-by-step evolution all but impossible. For instance... A wing isn’t just bones and feathers (or membrane). A wing requires a certain type of hollow bones, which the alleged ancestors of birds didn't have. And wings by themselves are useless - what reproductive benefit would wings have without the accompanying systems that lead to actual flight (the simultaneous requirements for bone pneumatization, muscle attachment sites, feather or membrane development, and the regulatory changes that control all of them)? Wings without these features would be harmful. Hollow bones without flight would be detrimental. The step-by-step path leading from non-bird to flying birds is filled with easily killed, unselectable intermediates. This is where evolutionists constantly fail - they look at modification in isolation, without considering that these systems are large, interconnected networks of functional parts all working together. And it all starts at the genetic level, from the DNA itself. DNA genes code for proteins. Regulatory information organizes when these proteins are built and how much should be made. Further regulatory systems coordinate where these proteins go after they’re built. And yet more informational networks place the proteins into the final system in coordination with other proteins. Then these protein systems are fit together to make entire organs, tissues, bones, etc. All of these systems and processes are coordinated from the DNA - which means major modification like turning a fish fin into a bird wing requires many coordinated DNA changes across the entire network. One change at a time simply cannot lead to the coordination of an entire multi-part coordinated system like this. A mutation that changes one protein would need another coordinated mutation to fit that mutated protein into the right place, which would require other proteins to be mutated to fit together into that system, which would also require yet more regulatory mutations to keep everything coordinated... Nothing works in isolation. It's all connected. Which is why it can't evolve one step at a time. One step at a time does nothing. Life requires all or nothing systems. Only intelligence can engineer all or nothing systems.

Divinely Designed

46,204 views • 3 days ago

Beauty should be a core pursuit of biotechnology. There should be companies and nonprofits that engineer organisms solely for the sake of crafting beautiful things. A few reasons why: 1/ Biotechnology has historically worked in reductionist ways, but many useful functions only emerge at the systems level. By engineering a systems-level outcome, like beauty, we will get much better at engineering organisms in predictable ways. When I say "reductionist," I mean that most useful things in biotechnology (drugs and tools) were discovered by stripping molecules from their natural contexts. Scientists collect organisms from soil or wherever and then study their molecules in isolation. This basic approach has yielded everything from rapamycin to antibiotics and CRISPR. This reductionism, though, means that that we know disturbingly little about how life actually works at a systems-level. My core argument is that, by studying beauty, we can remedy this. Beauty has persisted through tens of millions of years of evolution because it is functional; bright colors help attract pollinators to a plant, for example, which helps the plant breed. If evolution has created all of this beauty for functional reasons, then it stands to reason that by trying to create **new** forms of beauty, we'll be able to discover and understand how these systems-level functions work! Indeed, we may even be able to create entirely new functions that biology hasn't evolved yet. These functions will not possible to understand via isolated molecules or reductionism. Therefore, a company pursuing engineered beauty for the sake of beauty will probably make many fundamental discoveries about how organisms develop, interact, adapt to their surroundings, and so on. 2/ Beauty is a way to grow the field and bring more people into biotechnology. Nick Desnoyer’s flower design work, for example, has probably reached hundreds of thousands of people. The glowing plants from Light Bio, too, were featured in the mainstream press. You may not think that these examples are “important” for the universe relative to, say, an incrementally better cancer therapeutic, but there’s no question that they are way more popular to mainstream audiences and good, overall, for the field. 3/ The market is huge! Breeding is already widely used to engineer beauty, or at least to select for aesthetic preferences. Pugs are evolutionarily suboptimal, but they've been bred precisely to satisfy a certain aesthetic desire are now a multi-billion dollar industry. The Juliet Rose, developed via breeding over a 15-year period, debuted at the 2006 Chelsea Flower Show and is enormously profitable today. Why should deliberately engineered forms of beauty be any different? If you are building a biotech company or nonprofit that is pursuing beauty, please reach out! I’d love to help.

Niko McCarty.

18,291 views • 3 months ago