Lifeboat Foundation

Powner’s team didn’t check whether its sulfur-based catalysts had a chiral bias. That’s where Donna Blackmond, an origin of life chemist at Scripps Research, and her colleagues Min Deng and Jinhan Yu grabbed the baton. They tested two of Powner’s sulfur compounds to see whether the catalysts were sensitive to chirality as they formed dipeptides. They were, but not in the way Blackmond had expected. The catalysts created about four times as many “heterochiral” dipeptides—those pairing a left-handed amino acid (L) with a right-handed (D) one—as fully chiral products. “We thought it was bad news,” Blackmond says, because it suggested that even if amino acids on early Earth started with a bias, it would have been scrambled as proteins formed.

But as Blackmond and her colleagues looked more deeply, the news got better. In a series of experiments, the Scripps researchers started with skewed proportions of L and D amino acids—for example, 60% Ls and 40% Ds. The L, D and D, L heterochiral dipeptides formed most quickly, and as they did they pulled equal numbers of L and D amino acids out of the mix. Because of the baseline bias, eventually a predominance of Ls remained in the pool of unreacted amino acids, raising the likelihood of forming fully lefthanded dipeptides. “It’s like a domino effect,” Powner says. The first heterochiral reaction eventually encourages more homochirals to form. “And it’s a general process that works with all amino acids,” Powner says. Joyce adds: “It’s just math.”

Follow-up experiments suggested a second bias that amplifies the effect. The team found that heterochiral dipeptides precipitate out of a solution more quickly than homochiral ones, speeding the way to a relative abundance of either homochiral L, L or D, D pairs, depending the starting mix. Just why this precipitation bias occurs isn’t yet clear, Blackmond says. However, Joyce says, together with the other effect, “it beautifully fits the [experimental] data.” Blackmond adds: “The wrong answer turned out to be the right answer to get us to homochirality.”

Alex Rosenberg is professor of Philosophy at Duke University and has made several important contributions to the philosophy of science, biology, and social science.

0:00 intro.
2:53 scientism.
5:09 naturalism and the manifest image.
7:25 pragmatism.
10:40 intentionality.
12:38 objections to eliminativism and truth.
14:35 consciousness.
16:50 biological functions, purposes, and the selected effects theory.
22:28 reductionism.
28:05 causality.
31:02 multiple realizability.
35:13 math.
39:45 morality.
44:51 humanism, art, and history.

Continue reading “Thing in itself” »

From the spirals of shells to the layout of cells, a new class of shapes redefines nature’s complexity.

Last year, scientists discovered a mathematically perfect star system — and now, they’re looking into whether it might contain signs of alien tech.

Dubbed HD 110067, the star system located just 100 light-years from Earth has six exoplanets that are each perfectly spaced apart in the sort of mathematical harmony rarely seen in our chaotic Universe. In a paper published in the journal Nature last November, scientists listed off the astounding attributes of the system, which unfortunately did not include any planets in the so-called “habitable zone,” or distance from the orbit-inducing star that could support life as we know it here on Earth.

All the same, scientists aren’t done looking, and as radio astronomer and alien life-seeking expert Steve Croft of the University of Berkeley told Space.com, there’s no reason that advanced civilizations may not have visited HD 110,067 and potentially left some of their technology behind.

New theoretical work establishes an analogy between systems that are dynamically frustrated, such as glasses, and thermodynamic systems whose members have conflicting goals, such as predator–prey ecosystems.

A system is geometrically frustrated when its members cannot find a configuration that simultaneously minimizes all their interaction energies, as is the case for a two-dimensional antiferromagnet on a triangular lattice. A nonreciprocal system is one whose members have conflicting, asymmetric goals, as exemplified by an ecosystem of predators and prey. New work by Ryo Hanai of Kyoto University, Japan, has identified a powerful mathematical analogy between those two types of dynamical systems [1]. Nonreciprocity alters collective behavior, yet its technological potential is largely untapped. The new link to geometrical frustration will open new prospects for applications.

To appreciate Hanai’s feat, consider how different geometric frustration and nonreciprocity appear at first. Frustration defies the approach that physics students are taught in their introductory classes, based on looking at the world through Hamiltonian dynamics. In this approach, energy is to be minimized and states of matter characterized by their degree of order. Some of the most notable accomplishments in statistical physics have entailed describing changes between states—that is, phase transitions. Glasses challenge that framework. These are systems whose interactions are so spatially frustrated that they cannot find an equilibrium spatial order. But they can find an order that’s “frozen” in time. Even at a nonzero temperature, everything is stuck—and not just in one state. Many different configurations coexist whose energies are nearly the same.

Simple rules in simple settings continue to puzzle mathematicians, even as they devise intricate tools to analyze them.

Human coexistence depends on cooperation. Individuals have different motivations and reasons to collaborate, resulting in social dilemmas, such as the well-known prisoner’s dilemma. Scientists from the Chatterjee group at the Institute of Science and Technology Austria (ISTA) now present a new mathematical principle that helps to understand the cooperation of individuals with different characteristics. The results, published in PNAS, can be applied to economics or behavioral studies.

A group of neighbors shares a driveway. Following a heavy snowstorm, the entire driveway is covered in snow, requiring clearance for daily activities. The neighbors have to collaborate. If they all put on their down jackets, grab their snow shovels, and start digging, the road will be free in a very short amount of time. If only one or a few of them take the initiative, the task becomes more time-consuming and labor-intensive. Assuming nobody does it, the driveway will stay covered in snow. How can the neighbors overcome this dilemma and cooperate in their shared interests?

Scientists in the Chatterjee group at the Institute of Science and Technology Austria (ISTA) deal with cooperative questions like that on a regular basis. They use game theory to lay the mathematical foundation for decision-making in such social dilemmas.

In a recent development at Fudan University, a team of applied mathematicians and AI scientists has unveiled a cutting-edge machine learning framework designed to revolutionize the understanding and prediction of Hamiltonian systems. The paper is published in the journal Physical Review Research.

Named the Hamiltonian Neural Koopman Operator (HNKO), this innovative framework integrates principles of mathematical physics to reconstruct and predict Hamiltonian systems of extremely-high dimension using noisy or partially-observed data.

The HNKO framework, equipped with a unitary Koopman structure, has the remarkable ability to discover new conservation laws solely from observational data. This capability addresses a significant challenge in accurately predicting dynamics in the presence of noise perturbations, marking a major breakthrough in the field of Hamiltonian mechanics.

A mathematical historian at Trinity Wester University in Canada, has found use of a decimal point by a Venetian merchant 150 years before its first known use by German mathematician Christopher Clavius. In his paper published in the journal Historia Mathematica, Glen Van Brummelen describes how he found the evidence of decimal use in a volume called “Tabulae,” and its significance to the history of mathematics.

The invention of the decimal point led to the development of the decimal system, and that in turn made it easier for people working in multiple fields to calculate non-whole numbers (fractions) as easily as whole numbers. Prior to this new discovery, the earliest known use of the decimal point was by Christopher Clavius as he was creating astronomical tables—the resulting work was published in 1593.

The new discovery was made in a part of a manuscript written by Giovanni Bianchini in the 1440s—Van Brummelen was discussing a section of trigonometric tables with a colleague when he noticed some of the numbers included a dot in the middle. One example was 10.4, which Bianchini then multiplied by 8 in the same way as is done with modern mathematics. The finding shows that a decimal point to represent non-whole numbers occurred approximately 150 years earlier than previously thought by math historians.