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My All-Time Favorite Science Discovery June 1, 1984—forty years ago today—is when it would be fair to say I made my all-time favorite science discovery. Like with basically all significant science discoveries (despite the way histories often present them) it didn’t happen without several long years of buildup. But June 1, 1984, was when I […]
9 months ago

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More from Stephen Wolfram Writings

Towards a Computational Formalization for Foundations of Medicine

A Theory of Medicine? As it’s practiced today, medicine is almost always about particulars: “this has gone wrong; this is how to fix it”. But might it also be possible to talk about medicine in a more general, more abstract way—and perhaps to create a framework in which one can study its essential features without […]

a month ago 22 votes
Launching Version 14.2 of Wolfram Language & Mathematica: Big Data Meets Computation & AI

The Drumbeat of Releases Continues… Notebook Assistant Chat inside Any Notebook Bring Us Your Gigabytes! Introducing Tabular Manipulating Data in Tabular Getting Data into Tabular Cleaning Data for Tabular The Structure of Tabular Tabular Everywhere Algebra with Symbolic Arrays Language Tune-Ups Brightening Our Colors; Spiffing Up for 2025 LLM Streamlining & Streaming Streamlining Parallel Computation: […]

a month ago 36 votes
Who Can Understand the Proof? A Window on Formalized Mathematics

Related writings: “Logic, Explainability and the Future of Understanding” (2018) » “The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics” (2022) » “Computational Knowledge and the Future of Pure Mathematics” (2014) » The Simplest Axiom for Logic Theorem (Wolfram with Mathematica, 2000): The single axiom ((a•b)•c)•(a•((a•c)•a))c is a complete axiom system for Boolean algebra (and […]

2 months ago 75 votes
Useful to the Point of Being Revolutionary: Introducing Wolfram Notebook Assistant

Note: As of today, copies of Wolfram Version 14.1 are being auto-updated to allow subscription access to the capabilities described here. [For additional installation information see here.] Just Say What You Want! Turning Words into Computation Nearly a year and a half ago—just a few months after ChatGPT burst on the scene—we introduced the first […]

3 months ago 86 votes
Foundations of Biological Evolution: More Results & More Surprises

This is a follow-on to Why Does Biological Evolution Work? A Minimal Model for Biological Evolution and Other Adaptive Processes [May 3, 2024]. Even More from an Extremely Simple Model A few months ago I introduced an extremely simple “adaptive cellular automaton” model that seems to do remarkably well at capturing the essence of what’s […]

3 months ago 71 votes

More in science

Robotaxis Are Here

Within 1-5 years, our daily transportation will be upended, and cities will be reshaped.

12 hours ago 1 votes
The 2025 Wolf Prize in Physics

One nice bit of condensed matter/nanoscale physics news:  This year's Wolf Prize in Physics has gone to three outstanding scientists, Jim Eisenstein, Moty Heiblum, and Jainendra Jain, each of whom have done very impactful work involving 2D electron gases - systems of electrons confined to move only in two dimensions by the electronic structure and alignment of energy bands at interfaces between semiconductors.  Of particular relevance to these folks are the particularly clean 2D electron gases at the interfaces between GaAs and AlGaAs, or in GaAs quantum wells embedded in AlGaAs. A thread that connects all three of these scientists is the fractional quantum Hall effect in these 2D systems.  Electrons confined to move in 2D, in the presence of a magnetic field perpendicular to the plane of motion, form a remarkable system.  The quantum wavefunction of an electron in this situation changes as the magnetic induction \(B\) is increased.  The energy levels of such an electron are given by \((n+1/2)\hbar \omega_{c}\), where \(\omega_c \equiv eB/m*\) is the cyclotron frequency.  These energy levels are called Landau Levels.  The ratio between the 2D density of electrons and the density of magnetic flux in fundamental units (\(B/(h/e)\)) is called the "filling factor", \(\nu\), and when this is an integer, the Hall conductance is quantized in fundamental units - see here.   Figure 4 from this article by Jain, with \(R_{xx}(B)\) data from here.  Notice how the data around \(B=0\) looks a lot like the data around \(\nu = 1/2\), which looks a lot like the data around \(\nu=1/4\).  A remarkable thing happens when \(\nu = 1/2\) - see the figure above.  There is no quantum Hall effect there; in fact, if you look at the longitudinal resistance \(R_{xx}\) as a function of \(B\) near \(\nu = 1/2\), it looks remarkably like \(R_{xx}(B)\) near \(B = 0\).  At this half-integer filling factor, the 2D electrons plus the magnetic flux "bundle together", leading to a state with new low-energy excitations called composite fermions that act like they are in zero magnetic field.  In many ways the FQHE looks like the integer quantum Hall effect for these composite fermions, though the situation is more complicated than that.  Jainendra Jain did foundational work on the theory of composite fermions, among many other things. Jim Eisenstein has done a lot of great experimental work involving composite fermions and even-denominator FQH states.  My postdoctoral mentor, Bob Willett, and he are first two authors on the paper where an unusual quantum Hall state was discovered at \(\nu = 5/2\), a state still under active investigation for potential topological quantum computing applications.   One particularly surprising result from Eisenstein's group was the discovery that some "high" Landau level even-denominator fillings (\(\nu = 9/2, 11/2\)) showed enormously anisotropic resistances, with big differences between \(R_{xx}\) and \(R_{yy}\), an example of the onset of a "stripe" phase of alternating fillings.   Another very exciting result from Eisenstein's group used 2D electron gases in close proximity parallel layers and in high magnetic fields, as well as 2D electron gases near 2D hole gases.  Both can allow the formation of excitons, bound states of electrons and holes, but with the electrons and holes in neighboring layers so that they could not annihilate each other.  Moreover, a Bose-Einstein condensation of those excitons is possible leading to remarkable superflow of excitons and resonant tunneling between the layers.  This review article is a great discussion of all of this. Moty Heiblum's group at the Weizmann Institute has been one of the world-leading groups investigating "mesoscopic" physics of confined electrons in the past 30+ years.  They have performed some truly elegant experiments using 2D electron gases as their platform.  A favorite of mine (mentioned in my textbook) is this one, in which they make a loop-shaped interferometer for electrons which shows oscillations in the conductance as they thread magnetic flux through the loop; they then use a nearby quantum point contact as a charge sensor near one arm of the interferometer, a which-path detector that tunably suppresses the quantum interference.  His group also did foundational work on the use of shot noise as a tool to examine the nature and transport of charge carriers in condensed matter systems (an idea that I found inspiring).  Their results showing that the quasiparticles in the fractional quantum Hall regime can have fractional charges are remarkable.  More recently, they have shown how subtle these measurements really can be, in 2D electron systems that can support neutral excitations as well as charged ones. All in all, this is a great recognition of outstanding scientists for a large volume of important, influential work. (On a separate note:  I will be attending 3+ days of the APS meeting next week.  I'll try to do my usual brief highlight posts, time permitting.  If people have suggestions of cool content, please let me know.)

2 hours ago 1 votes
Flipping the switch on far-UVC

We’ve known about far-UVC’s promise for a decade. Why isn't it everywhere?

2 days ago 5 votes
Why Do Researchers Care About Small Language Models?

Larger models can pull off greater feats, but the accessibility and efficiency of smaller models make them attractive tools. The post Why Do Researchers Care About Small Language Models? first appeared on Quanta Magazine

2 days ago 3 votes
Stem Cells for Parkinson’s Disease

For my entire career as a neurologist, spanning three decades, I have been hearing about various kinds of stem cell therapy for Parkinson’s Disease (PD). Now a Phase I clinical trial is under way studying the latest stem cell technology, autologous induced pluripotent stem cells, for this purpose. This history of cell therapy for PD […] The post Stem Cells for Parkinson’s Disease first appeared on NeuroLogica Blog.

2 days ago 3 votes