this post was submitted on 20 Nov 2023
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Science

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[–] [email protected] 48 points 1 year ago (2 children)

For those wondering the others are:

  • M(0) = 2
  • M(1) = 3
  • M(2) = 6
  • M(3) = 20
  • M(4) = 168
  • M(5) = 7581
  • M(6) = 7828354
  • M(7) = 2414682040998
  • M(8) = 56130437228687557907788

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.

[–] [email protected] 7 points 1 year ago (2 children)

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.

[–] [email protected] 11 points 1 year ago (1 children)
[–] [email protected] 1 points 1 year ago (1 children)

Typing isn't saying!

I win!!

[jk]

[–] [email protected] 1 points 11 months ago

Yes, jk rowling

[–] [email protected] 1 points 11 months ago
[–] [email protected] 4 points 1 year ago

So your end egg count after a run of Eggs, Inc. Got it.

[–] [email protected] 42 points 1 year ago (2 children)

EL5 why this is significant, please.

( Not trying to be any which way.)

[–] [email protected] 83 points 1 year ago (6 children)

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.

[–] [email protected] 30 points 1 year ago

Ah, yes, those things, of course.

[–] [email protected] 21 points 1 year ago

Glad we cleared that up. In hindsight, it was pretty obvious from the start.

[–] [email protected] 21 points 1 year ago (1 children)

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

[–] [email protected] 19 points 1 year ago

I understood most of the words, just the ones that I didn't made the rest incomprehensible garbledygoop

[–] [email protected] 9 points 1 year ago* (last edited 1 year 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 really did something here

[–] [email protected] 8 points 1 year ago* (last edited 1 year ago) (1 children)

rapidly growing

1 found in 32 years

[–] [email protected] 6 points 1 year ago (1 children)

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.

[–] [email protected] 2 points 11 months ago

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!

[–] [email protected] 2 points 1 year ago

Long slaughtering necromancer math

[–] [email protected] 46 points 1 year ago (3 children)

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.

[–] [email protected] 17 points 1 year ago (1 children)

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

[–] [email protected] 10 points 1 year ago

Mathmagicians.

[–] [email protected] 6 points 1 year ago* (last edited 1 year ago) (1 children)

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.

[–] [email protected] 5 points 1 year ago (1 children)

"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)

[–] [email protected] 7 points 1 year ago

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.

[–] [email protected] 3 points 1 year 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.

[–] [email protected] 18 points 1 year ago (1 children)

Obligatory “it was down the back of the couch cushions”.

[–] [email protected] 16 points 1 year ago

Locked in the bottom of a disused filing cabinet, in and lavatory behind a locked door with a sign that said beware of jaguars

[–] [email protected] 18 points 1 year ago

"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."