Right and the point of defining this number as a non-repeating infinite sequence of 0s and 1s is just to show that non-repetition of digits alone is not sufficient to say a number contains all finite sequences.

Math kind of relies on assumptions, you really can’t get anywhere in math without an assumption at the beginning of your thought process.

That’s a decimal approximation of Pi with an ellipsis at the end to indicate its an approximation, not a definition. The way the ellipsis is used above is different. It’s being used to define a number via the decimal expansion by saying it’s an infinite sum of negative powers of 10 defined by the pattern before the ellipsis.

So we have:

0.101001000100001000001 . . . = 10^-1 + 10^-2 + 10^-3 + 10^-4 +10^-5+ . . .

Pi, however, is not defined this way. Pi can be defined as twice the solution of the integral from -1 to 1 of the square root of (1-x^2), a function defining a unit semi-circle.

Implicitly defining a number via it’s decimal form typically relies on their being a pattern to follow after the ellipsis. You can define a different number with twos in it, but if you put an ellipsis at the end you’re implying there’s a different pattern to follow for the rest of the decimal expansion, hence your number is not the same number as the one without twos in it.

It’s implicitly defined here by its decimal form:

0.101001000100001000001 . . .

The definition of this number is that the number of 0s after each 1 is given by the total previous number of 1s in the sequence. That’s why it can’t contain 2 despite being infinite and non-repeating.

Veritasium

Sucks about this guy, he used to actually make interesting pop-sci videos without mangling the concepts and conclusions too badly. It was a breath of fresh air compared to the bullshit other science popularizers like Michio Kaku were dreaming up at the time. But nowadays his videos all have these extremely vague clickbait titles. And much worse than that: he clearly shills tech from sponsored companies. Not with marked sponsorship segments, but with entire videos that are essentially long form advertisements with all of the disinformation marketing entails. Other than the word sponsor being highlighted and placed before the title, there is no indication for his audience that they shouldn’t view such sponsored videos as normal Veritasium videos.

The most blatant example of this was when he shilled for Waymo self driving ride share cars in an 18 minute video they sponsored. It was about two years ago, the title:

Why You Should Want Driverless Cars On Roads Now

Here’s a video detailing the ways in which Veritasium misleads his audience to produce corporate propaganda using the driverless car video as its main example. It’s an hour long, but I still recommend giving it a watch because it’s so thorough: https://www.youtube.com/watch?v=CM0aohBfUTc

I’m sure Veritasium does still make good, well researched and well intentioned videos, but after seeing the way he intentionally manipulates his audience in certain videos, I can’t help but be distrustful of everything he says elsewhere.

Yep, and it’s a lot more successful than you’d think. I’ve been using it for over a year now and I literally have not come across a sponsored video yet that hasn’t had its sponsored segments reported. Not even on videos that were uploaded literally 10 minutes ago. Highly recommend

Congrats, that already exists as a browser addon and it’s free. Look up sponsorblock.

Hard embedding ads works for live streams since you can’t know when exactly any given ad will start or end. If Youtube were to do this, it would be very trivial for sponsorblock to simply take on the role of adblocker since the community would be able to report the location of the ads.

I don’t have much experience with cocaine or stimulants in general, but I have gone through the ringer of opioid addiction. I’m five years clean now thanks to Buprenorphine.

From that horrific experience, my gut feeling is that there is no possible way sugar is anywhere near as addictive as opioids. At least not for anyone predisposed to enjoying opioids, of course. Going through opioid withdrawal is a horror I will wish on very few people. It has broken me before, and it has broken some of the strongest people I’ve ever known. I have never felt an incredible urge to steal from my own family to satisfy a sweet tooth, that’s for sure.

Advertising. Literally all of it.

That’s such a great idea that I’m sure anyone who did this would end up charged with some type of fraud, unfortunately

Pay off my debt, buy a modest home, go back to school, never work a shit job for minimum wage ever again.

But I don’t need anywhere near 20,000,000 dollars a year to do that.

After some large donations to communist organizations, I’d put the remaining few million per year into buying commercial slots on every major TV network in the US. Then I’d create Jury Nullification PSAs and blast them over the airways continuously until the message sinks in universally that juries are under no obligation at all to respect the laws currently grinding marginalized people into dust.

I think it’s most to do with exactly how much wealth a person was born into.

Someone who is constantly on the verge of being homeless, possibly even starving, will very soon get desperate enough to do things they aren’t proud of to survive.

On the other hand, someone born into immense wealth will have very little understanding of people who are struggling. That’ll make it very hard for them to empathize. And with all that power, their sheer indifference will have them crushing the poor under their boots like ants. This is highly exacerbated by the fact that it is in their best interest to support policy that transfers wealth upwards.

I like that North Korea has turned the Truman Show into a real thing all for the sake of western tourists. It takes a serious dedication to the art of theater and acting to transform an entire country of 26 million people into an endless and infinitely deep stage production. They’ve built full skyscrapers just as back drops for their sets. They painstakingly carved and painted millions upon millions of wooden props to resemble food items such as fruit, vegetables, and grains to place in store sets ubiquitously since real food no longer exists there. The wide assortment of actors walking the streets and pretending to go to work and do their jobs, each of them with their own unique backstory handcrafted to resemble the life of a real person. The fact that they’ve maintained the illusions of functioning trains by using clever line of sight techniques to hide the dozens of stage crew that need to push the cars along the tracks.

This is a very impressive accomplishment once you consider 90% of the country is currently being held in concentration camps for disrespecting the Kim dynasty by not maintaining the same haircut as their supreme leader. That the remaining 10 percent can put on this kind of show is spectacular without any kind of monetary compensation or even food. Everyone there is starving to death, but they’ve managed to hide such inadequacies through industrious makeup and lighting techniques. The country’s dedication is so intense even that these actors are allowed to have their own haircuts so as to not hurt immersion.

I would pirate even if it were stealing. In fact, if a company lost real money every time I pirated something, I would make an effort to pirate more often.

Run around dressed as a bat beating people to a vegetative state

Batman’s no kill policy is definitely not for any kind of moral objection to taking lives, that’s for sure. He brutalizes normal ass people with extreme excessive force on the regular. There’s no chance that none of these people succumb to their injuries soon after. It’s probably just to make himself feel better about it, a cope that allows him to justify it all by saying he didn’t necessarily inflict mortal wounds on purpose.