https://www.sciencealert.com/mathematicians-have-found-the-ninth-dedekind-number-after-32-years-of-searching
Undeterred after three decades of looking, and with some assistance from a supercomputer, mathematicians have finally discovered a new example of a special integer called a Dedekind number.
For those wondering the others are:
And our new one M(9) = 286386577668298411128469151667598498812366
That is two hundred eighty-six duodecillion, three hundred eighty-six undecillion, five hundred seventy-seven decillion, six hundred sixty-eight nonillion, two hundred ninety-eight octillion, four hundred eleven septillion, one hundred twenty-eight sextillion, four hundred sixty-nine (noice) quintillion, one hundred fifty-one quadrillion, six hundred sixty-seven trillion, five hundred ninety-eight billion, four hundred ninety-eight million, eight hundred twelve thousand, three hundred sixty-six.
That is two hundred eighty-six duodecillion, three hundred eighty-six undecillion, five hundred seventy-seven decillion, six hundred sixty-eight nonillion, two hundred ninety-eight octillion, four hundred eleven septillion, one hundred twenty-eight sextillion, four hundred sixty-nine quintillion, one hundred fifty-one quadrillion, six hundred sixty-seven trillion, five hundred ninety-eight billion, four hundred ninety-eight million, eight hundred twelve thousand, three hundred sixty-six.
Now say it three times, fast.
I looked it up on Wikipedia.
In mathematics, the Dedekind numbers are a rapidly growing sequence of integers named after Richard Dedekind, who defined them in 1897. The Dedekind number M(n) is the number of monotone boolean functions of n variables. Equivalently, it is the number of antichains of subsets of an n-element set, the number of elements in a free distributive lattice with n generators, and one more than the number of abstract simplicial complexes on a set with n elements.
Pretty simple to understand. I mean, I understand it, for sure. Totally.
I understood most of the words, just the ones that I didn't made the rest incomprehensible garbledygoop
Good work everyone. I stay more with the stereo boolean variables, but the news about those lattices being free now is really great stuff. We really did something here
Lol, I thought that at first, but I'm pretty sure it's in how much larger the next number is to the last one.
Yes that's what it means, what is rapidly growing is the value of the next number in the sequence, not the amount of numbers we discovered!
Complements of GPT:
Imagine you have a puzzle with a set of rules about how you can put the pieces together. This puzzle isn't made of typical jigsaw pieces, but instead uses ideas from math to decide how they fit. A Dedekind number is like counting how many different ways you can complete this puzzle.
In simple terms, a Dedekind number is connected to a concept in mathematics called a "Boolean function." This is a type of math problem where you only use two things: yes or no, true or false, or in math language, 0 or 1. A "monotone Boolean function" is a special kind of this problem where changing a 0 to a 1 in your problem can only change the answer from 0 to 1, not the other way around.
The big news is that mathematicians and computer scientists just found a new, very large Dedekind number, called D(9). It took them 32 years since the last one was found! To find it, they used a supercomputer that can do lots of calculations at the same time. This was a big deal because Dedekind numbers are really hard to calculate. The numbers involved are so huge that it wasn't even sure if we could find D(9).
You can think of finding a Dedekind number like playing a game with a cube where you color the corners either red or white, but you can't put a white corner above a red one. The goal of the game is to count all the different ways you can do this coloring. For small cubes, it's easy, but as the cube gets bigger (like going from D(8) to D(9)), it becomes super hard.
So, discovering D(9) is a big achievement in mathematics. It's like solving a super complex puzzle that very few people can understand, let alone solve. It's significant because it pushes the boundaries of what we know in math and shows how powerful computers can help us solve really tough problems.
That seems more just very resource requiring than hard to do, in a modern world with computers? I get that these were ridiculous to find around 1900 when they were discovered and you had to find them without computers to do the calculations.
"Resource requiring" and "hard to do" are kind of the same in math's terms. Most unsolved math problems are either because we lack the resources, we lack observation (in case of phisics) or we lack both.
hat useful purpose does these Dedekind numbers have? Nothing, just like when lasers were first discovered (now we use them for medical and tech purposes)
You can kind of use this as a benchmark for where we are computationally as a society. If you plot these achievements on a graph, maybe we can plot the trajectory of achievement and predict where we will be in 10 years…or something.
🤔 That could matter a lot for chip designers. They'd need to know the ways in which a Boolean function could do such a thing since you use Boolean math to design the chips, and need to understand the math to design the chips in certain ways depending on your needs.
"What is a Dedekind number?"
"it is the number of antichains of subsets of an n-element set, the number of elements in a free distributive lattice with n generators, and one more than the number of abstract simplicial complexes on a set with n elements."
"Oh, why didn't you just say so? I thought the number of antichains of subsets of an n-element set, the number of elements in a free distributive lattice with n generators, and one more than the number of abstract simplicial complexes on a set with n elements was called something different. Of course I know what the number of antichains of subsets of an n-element set, the number of elements in a free distributive lattice with n generators, and one more than the number of abstract simplicial complexes on a set with n elements is, silly me."
Locked in the bottom of a disused filing cabinet, in and lavatory behind a locked door with a sign that said beware of jaguars
Is there a purpose to this, or is it just a bunch of math nerds justifying their college debts to themselves?
Like those physicists back in the day just playing around with useless toys messing with meaningless stuff like electricity and shit.
Mathematics is full of formulas and theories that were developed without a specific application in mind, but later found to be incredibly useful in various fields. Here's a list of some notable examples from ChatGPT :
Complex Numbers and Euler's Formula: Initially seen as abstract and theoretical, they're now fundamental in electrical engineering and quantum physics.
Fourier Transform: Originally developed for heat transfer problems, it's now crucial in signal processing, image analysis, and quantum physics.
Non-Euclidean Geometry: Once considered purely theoretical, it's essential in the theory of relativity and global positioning systems (GPS).
Group Theory: Developed as a part of abstract algebra, it's now instrumental in physics, chemistry (especially crystallography), and cryptography.
Graph Theory: Originating from a recreational math problem, it's now key in computer science, network analysis, and biology.
Number Theory: Initially pursued for its intellectual challenge, it's fundamental in modern cryptography, like RSA encryption.
Calculus of Variations: Beginning as a mathematical curiosity, it's now used in physics, economics, and engineering to solve optimization problems.
Riemannian Geometry: Originally abstract in nature, it's crucial in general relativity and the description of spacetime.
Boolean Algebra: Developed from logic studies, it's the backbone of digital circuit design and computer science.
Set Theory and Cantor's Diagonal Argument: Seemingly abstract concepts, they're now foundational in computer science and logic.
Reminds me of an old 'The Far Side Cartoon.' A few cavemen sitting around a fire, and one standing off by himself.
"Pfft! Just another dumb fad."
You've had a couple of pretty good responses. I would add that the very fact that you can ask that question demonstrates a failure of the education system and the fundamental problem of depending on business ideals to manage society.
In the first case, a proper education would have included, at all grade levels, examples and discussion of the various purely intellectual pursuits that ultimately proved critical to some technological advance that improved quality of life.
In the second case, the naive "businessification" of society means that any pursuit that doesn't make clear at the outset what practical (ie profitable) goal is being pursued is dismissed as folly unworthy of funding and support and education. (See my point above.)
Math nerds don’t need to justify their college debt to themselves. The math alone was enough.
The purpose is to live a life doing what they love and getting paid oodles for it knowing jealous whiners like you are wasting their existences flipping burgers and getting emotionally abused by Karens.
Unless you thought your shitty McDonald's manager job had any real purpose.