Comment on Mathematicians Have Found The Ninth Dedekind Number, After 32 Years of Searching

Tok0@sh.itjust.works ⁨11⁩ ⁨months⁩ ago

• chunkystyles@sopuli.xyz ⁨11⁩ ⁨months⁩ ago

  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.

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  • Scrof@sopuli.xyz ⁨11⁩ ⁨months⁩ ago

    Ah, yes, those things, of course.

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  • Snowcano@startrek.website ⁨11⁩ ⁨months⁩ ago

    Ah, yes. I know some none of these words.

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  • PowerGloveSoBad@lemmy.world ⁨11⁩ ⁨months⁩ ago

    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 did it

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  • Jackcooper@lemmy.world ⁨11⁩ ⁨months⁩ ago

    rapidly growing 1 found in 32 years

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• fossilesque@mander.xyz ⁨11⁩ ⁨months⁩ ago

  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.

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  • swab148@startrek.website ⁨11⁩ ⁨months⁩ ago

    I still don’t understand it, but good job math wizards!

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  • pinkdrunkenelephants@lemmy.cafe ⁨11⁩ ⁨months⁩ ago

    🤔 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.

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