Any time you see a video of a cat backing up and saying “no no no no no” it’s because they’re watching the researcher’s hand move toward the on switch of that centrifuge.
A couple years ago my chemistry teacher told my class that the Egyptians had really advanced technology (technology even more advanced than our own) thousands of years ago but it all got lost because they started a nuclear war
Edit: she told us that the evidence was that there were smartphone paintings
Aren’t there numbers past (plus/minus) infinity? Last I hear there’s some omega stuff (for denoting numbers “past infinity”) and it’s not even the usual alpha-beta-omega flavour.
Come to think of it, is there even a notation for “the last possible number” in math? aka something that you just can’t tack “+1” at the end of to make a new number?
The smallest infinity is the size of the natural numbers. That infinty, Aleph zero, is smaller than the infinity of the real numbers, Aleph one. “etc.”
As for your second question, I don’t think any “last number” could exist unless we explicitly declared one. And even then… I’m not sure what utility there would be in declaring a “last number”.
There is nothing “past” infinity, infinity is more a concept than a number, there are however many different kinds of infinity. And for the record, infinity + 1 = infinity, those are completely equal. Infinity + infinity = infinity x 2 = still the same kind of infinity. Infinity times infinity is debatably a different kind of infinity but there are fairly simple ways of showing it can be counted the same.
Essentially the number of numbers between 1 and 2 is the same as the number of numbers between 0 and infinity. They are still infinite.
You have the spirit of things right, but the details are far more interesting than you might expect.
For example, there are numbers past infinity. The best way (imo) to interpret the symbol ∞ is as the gap in the surreal numbers that separates all infinite surreal numbers from all finite surreal numbers. If we use this definition of ∞, then there are numbers greater than ∞. For example, every infinite surreal number is greater than ∞ by the definition of ∞. Furthermore, ω > ∞, where ω is the first infinite ordinal number. This ordering is derived from the embedding of the ordinal numbers within the surreal numbers.
Additionally, as a classical ordinal number, ω doesn’t behave the way you’d expect it to. For example, we have that 1+ω=ω, but ω+1>ω. This of course implies that 1+ω≠ω+1, which isn’t how finite numbers behave, but it isn’t a contradiction - it’s an observation that addition of classical ordinals isn’t always commutative. It can be made commutative by redefining the sum of two ordinals, a and b, to be the max of a+b and b+a. This definition is required to produce the embedding of the ordinals in the surreal numbers mentioned above (there is a similar adjustment to the definition of ordinal multiplication that is also required).
Note that infinite cardinal numbers do behave the way you expect. The smallest infinite cardinal number, ℵ₀, has the property that ℵ₀+1=ℵ₀=1+ℵ₀. For completeness sake, returning to the realm of surreal numbers, addition behaves differently than both the cardinal numbers and the ordinal numbers. As a surreal number, we have ω+1=1+ω>ω, which is the familiar way that finite numbers behave.
What’s interesting about the convention of using ∞ to represent the gap between finite and infinite surreal numbers is that it renders expressions like ∞+1, 2∞, and ∞² completely meaningless as ∞ isn’t itself a surreal number - it’s a gap. I think this is a good convention since we have seen that the meaning of an addition involving infinite numbers depends on what type of infinity is under consideration. It also lends truth to the statement, “∞ is not a number - it is a concept,” while simultaneously allowing us to make true expressions involving ∞ such as ω>∞. Lastly, it also meshes well with the standard notation of taking limits at infinity.
Hi, I’m a mathematician. My specialty is Algebra, and my research includes work with transfinites. While it’s commonly said that infinity “isn’t a number” I tend to disagree with this, since it often limits how people think about it. Furthermore, I always find it odd when people offer up alternatives to what infinity is; are numbers never concepts?
Regardless, here’s the thing you’re actually concretely wrong about: there are provably things bigger than infinity, and they are all bigger infinities. Furthermore, there are multiple kinds of transfinite algebra. Cardinal algebra behaves mostly like how you described, except every transfinite cardinal has a successor (e.g. There are countably many natural numbers and uncountably many complex numbers). Ordinal algebra, on the other hand, works very differently: if ω is the ordinal that corresponds to countable infinity, then ω+1>ω.
After reading how this thread is going I’m half expecting this to be a Kurzgesagt video or something equally “cutesy existential dread” inducing lol. Let’s see what do I find!
I’ve been making six figures while getting my PhD. There are plenty of opportunities to get your PhD funded if you are a US citizen. There are plenty more valid places to poke fun at pursuing a PhD but it is very common to have funding and thus no debt.
Like the guy who found this somehow important new shape not to long ago? I don’t think he has a PhD. But he did contribute. Not saying that it’s easy though.
Presumably you could meet the boundary with “a dollah fifty in late fees at the public library” and find a way to push through from there. You’d have to find a way to publish or share your new knowledge. Studying at uni gives you access to experts in their own thing that likely have knowledge that could help you with your thing as well as a system designed to churn out these papers when you eventually find your thing.
Every day people discover new things but it takes attention, effort, and will to PROVE it’s a new thing and more yet to share that with the world. Too bad you can’t get an honorary PhD for doing that, at least not reliably.
It’s funny but you see the same thing in sports, or I see it specifically in hockey. Phenom kid gets drafted and at 18 has the social skills of the hockey puck he’s playing with. By the time he’s 36 he’s not the player he once was but is a more well rounded individual with age and experience. When you focus all your energy to become the best at something, like a PhD, athlete, musician, whatever, you sacrifice some things along the way for sure.
When u look at most people I feel like the trending alternative at 18-50 y is personality of a hockey puck and also skills of a hockey puck, with the reasoning ability of the hockey puck.
That’s not universally true. I know several people with PhD who have encyclopedic knowledge completely outside their specialisation. Some people are just super intelligent, talented and have enormous memory. The world is not fair.
The constant barrage of Joe Rogan clips of idiots claming it was impossible to move these huge stones over those distances with the tech at the time was what drove me to disable YouTube shorts.
Honestly, the first and arguably most important step is recognizing how much of online content is specifically designed to get a reaction out of you, primarily in the form pissing you off.
What’s funny (I guess funny lol) is ever since I got my current job about 2.5 years ago, I no longer need to use social media. I am much, much happier without it. But I still get into little fights on forums and I really wish I didn’t. Every now and then I resolve to be less hostile, and things really do improve, but somehow I always get dragged back into old habits. But I’m a little hesitant to completely abandon things like Kbin because they are often my only window into events/what is going on/my hobbies. Idk what the answer is.
Well, the fact that you have the self awareness to realize is a great place to be. Not sure what to say other than try to treat your body with respect and your mind will follow.
I honestly I’m surprised how much of a problem this is for people. All I’ve done is made sure to hit the “not interested” type buttons on YouTube and tiktok whenever they pop up, and I’ve run into next to nothing after like 3 times of doing that. Sometimes I’ll watch something the algorithm thinks is adjacent to ragebait or alt-right bullshit so it’ll try to feed it to me, and after not-interested’ing the video it goes back to feeding me the stuff I actually want…
Do people just not use those features or is my experience with the algorithms really that different?
I would also like entomologists to pronounce the insect orders properly. That ‘p’? It belongs to the ‘-ter’. It’s ‘pter’, for wing. As in ‘coleo-ptera’, the ‘shield wing’, not ‘col-e-OP-tera’. Or ‘neuro-ptera’, the ‘lace-wing’, not ‘neur-OP-tera’.
We actually put the accent on a syllable THAT DOESN’T FUCKING EXIST in the Greek.
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