![]() ![]() It looks like a simple, innocuous question, but that’s what makes it special. The Conjecture lives in the math discipline known as Dynamical Systems, or the study of situations that change over time in semi-predictable ways. So, we might be working on it for decades longer. But he most likely can’t adapt his methods to yield a complete solution to the problem, as Tao subsequently explained. Tao’s recent work is a near-solution to the Collatz Conjecture in some subtle ways. The Conjecture is that this is true for all natural numbers (positive integers from 1 through infinity). You eventually land on 1, for every number we’ve ever checked. Take any natural number, apply f, then apply f again and again. And while the story of Tao’s breakthrough is promising, the problem isn’t fully solved yet.Ī refresher on the Collatz Conjecture: It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. As there is no tag for the latter, I created the tag "physical-constants".In September 2019, news broke regarding progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. ![]() However this question, and several others over the past few years, specifically concern the current physical constants functionality. N.B.: There is a tag for the deprecated "physicalconstants-package". For a discussion of the relative utility of performing calculations with exact vs. ![]() However, in its place, you can use eitherġ/(4 Pi where "AUsOf" means "angular units of", and = A key difference between the two is that "ElectricConstant" evaluates to a ratio of integers (which means it is treated as an "exact number" in Mathematica's internal calculations), while "AUsOfElectricPermittivity" evaluates to a floating point number, so if you would like only exact numbers in your calculation, you should use the former. $\frac$ is the vacuum permittivity, aka the electrical constant (see ). ![]() Thus we have: "AvogadroConstantNewSI", "BoltzmannConstantNewSI", "Elementar圜hargeNewSI", and "PlanckConstantNewSI". These are identified by the suffix "NewSI". But, in the absence of documentation, that's just an educated Several of the physical constants are available in alternate versions, as ratios of integers, which I assume is to allow exact calculations using physical constants. Based on the name, I would have expected "AvogadroConstantValueFoxHill" to be the dimensionless version of "AvogadroConstantFoxHill". What's supposed to be the difference between "AvogadroConstantFoxHill" and "AvogadroConstantValueFoxHill"? The following code, modified from the documentation for QuantityVariablePhysicalQuantity, gives the number of physical quantities ( including physical constants) in each of several categories, but only for those physical quantities present in MMA's built-in formulae. MSE member Mark Adler supplied this code, which gives a list of all units, including the physical constants, and then manually pulled out most (but not all) of the physical constants from it (http : // /questions/130049/physical - and - other - tried finding characteristics that would distinguish the physical constants from the other units, and would thus allow me to extract the physical constants alone, but was unsuccessful. Is there a way to generate a list of just the physical constants? N.B.: I've bolded the questions to make it easy to find them among the background verbiage. ![]()
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