Azrann

"Where did you come up with this convoluted plot?"

Some points of interest:

Corporate profits are soaring. After taxes, they now take 12.3 percent of national output, far above their postwar average of 7.3 percent.

Adjusted for inflation, hourly wages have risen 3 percent since the end of 2019, Ip noted. Corporate profits over the same period have risen 50 percent.

The Economic Policy Institute calculates that since 1979 the productivity of American workers has grown 90 percent while the pay of the typical worker has grown 33 percent. Had wages tracked output, the average worker would earn $16.40 more an hour today.

The profits are concentrated among the largest corporations. Earnings at the 500 biggest US firms rose 28 percent in the first quarter from a year earlier, the fastest pace since 2021, and their profit margins reached 14.8 percent. The seven technology giants known as the “Magnificent 7”—Apple, Microsoft, Nvidia, Alphabet, Amazon, Meta and Tesla—grew their profits 63 percent.

OH BOY OH BOY I GET TO EXPLAIN 3X + 1

So just “3x +1″ is an expression, not an equation, however it’s also shorthand for an infamous mathematical problem known as the “Collatz Conjecture”. It’s a very, very, VERY simple question that still has mathematicians scratching their heads.

The premise goes like this:

Take a number (a positive integer) and call it “x”.

If that number is even, divide it by 2. If the number is odd, then multiply it by 3 and then add 1 (3x + 1). Repeat over and over again. (so you could go 3, 3(3) + 1 = 10, 10/2 = 5, 3(5) + 1 = 16, etc.)

The Collatz Conjecture (aka the 3x + 1 problem) states that eventually, this sequence will always lead you to the number 1 where it loops 1=>4=>2=>1=>4=>2=>1=>4=>2=>1 forever, regardless of which number you start this sequence with.

Now, there is no proof that this is true or false yet (hence the “conjecture” part).

If you want to disprove the 3x + 1 problem, all that you have to do is find a positive integer that does not ever make it to 1, either by finding a closed loop of numbers that ISNT 1=>4=>2=>1 or by finding a value that just has it keep increasing to infinity (7=>22=>11=>34=>17=>52=>27=>82=>41=>122…..while this sequence does end up coming back down to 1, people theorize there could be a starting point where it just keeps going up and up and up forever). If you can just find ONE, then you will have successfully solved 3x + 1.

But to this day, every single positive integer has been tested from 1 to 2^68 (or approx. 1-300,000,000,000,000,000,000 (300 quintillion). None of them have proven to be an exception.

But any Cookie Clicker veteran knows that 300 quintillion is child’s play. A number that makes an infinitesimal speck of dust look like a god damn multiverse in relation to infinity. And we don’t exist outside of time (yet) so we probably aren’t going to be able to test an infinite number of positive integers.

So if you want to prove the 3x + 1 problem, you gotta make a proof. If you’ve never done mathematical proofs before or don’t know what they are, remember back in school when your teacher gave you those “Solve for x:” questions and you had to move numbers and variables around until you got the right answer? Yeah, you gotta do that. A lot. And you MIIIIIGHT be able to get to the right answer. That triple dot thing from Beginner’s Guide shows up there although it’s upside down apologies I am very tired, and like the Beginner’s Guide, crying once or twice is completely normal and even expected.

But no one has been able to make a proof yet. So there 3x + 1 stands to this day. The most deceptively simple math question that has stumped mathematicians for decades. If you want a more in-depth talk about this problem, this video does a fantastic job going into the details.