This post is so true. I work in local government in a state that has TONS of money, yet our systems to control the information for agents to determine if you keep your kids or not is still based on MS-DOS. it’s insane to see in 2023
Using something like DOS is neither preferred nor more safe. Last time MS DOS received a security patch was 23 years ago. It’s open to pretty much any security vulnerability you can think of. In case you depend on a DOS app it’s preferable to run it on a modern OS that is DOS compatible, windows 10 32bit for example (I believe Win11 still has support). Or even better sandboxed in an emulator like DOSBox on a more secure OS.
I really don’t want to rely on security through obscurity… MS-DOS was written back when every programmer trusted everything that ran on the computer, security wasn’t even an afterthought, and encryption was the sole domain of math nerds, conspiracy theorists, and the nerd equivalent of doomsday preppers because it was “too computationally expensive.” Its sole saving grace in terms of security is that it doesn’t support multitasking so malware can’t run in the background, but you can just target whatever software it’s running, instead.
If it works like telescopes, the Very Large Hadron Collider, then the Extremely Large Hadron Collider, and then the Overwhelmingly Large Hadron Collider.
There’s a five in six chance you are picked 1 out of X, and a one in six chance you are 10 out of X.
If you’ve been picked, there are three possible outcomes.
Flipping the lever kills you. 5/6 x 1/X
Flilling the lever saves you and 9 other people. 1/6 x 1/X
Flipping the lever does nothing at all. 1/6 x 9/X
From a purely statistical standpoint, you’re five times more likely to die flipping the lever, but the expected value, measured in lives saved, for flipping the lever is twice as high as not.
From a purely altruistic measure, you should always flip the lever, because at worst you kill yourself, at best you save 10 people, and you can do it with significant confidence that it doesn’t actually matter.
But back to my original question, 5/6X vs 1/6X vs 9/6X where as X approaches infinity, the difference becomes negligible.
Good question to ask, since specifics of selection process may affect the decision outcome! Other variants include growing humans in a vat from scratch on demand, using Star Trek transporter clones, or abducting the necessary number of people from a pre-selected list where your name happens to be the first one. For now, imagine the potential population as the 5 billion living cognizant adults.
as X approaches infinity, the difference becomes negligible
It may be negligible to the 4.999… billion adults sleeping comfortably and securely in their beds tonight, but the problem presupposed that you have already been abducted. It remains underdefined whether you refers to you the specific person reading this meme, or a more general you-the-unfortunate who has been chosen and is now listening to this on the headphones.
That’s assuming the villain who is trying to deny you information by the blindfold and earplugs was dumb enough to put them close together that a spit would reach a neighbor.
It depends. They both contract, but if the second pupil is small, it doesn’t matter. I have a small one, and it just causes uveitis every once in a while. I went half my life without even noticing it.
You can become sensitive to light, and the irritation can slowly cause blindness. That’s pretty much it
One fun thing: if you ever get uveitis, wearing an eye patch won’t work. Your eye will still try to dilate with your other eye. Also your pupil/s will stretch like in the pictures.
This is actually very interresting. I always found it hard to understand how some people can have so many sexual partners, and then there are people with very few of sexual partners. I had this theory that there must be some subculture of people who are really into this, date eachother in this group which causes their number to increase abnormally. It was just a silly theory but this sort of supports it?
If you look at this a little closer, you’ll notice that there aren’t actually that many highly connected nodes.
The big structure is mostly composed of single link chains.
Elsewhere it was mentioned that the researchers were also surprised by that, and did followup interviews that revealed that it was against social rules to date your exes partners ex. Basically two couples can’t “swap” partners. I thought it was interesting that you didn’t see that, but you do see a few triangles.
And that’s even more interesting. As someone who was not part of any of the graph in high school / college, how would a big link of chains play out in real time?
Like “The Mary and Tom met at a party. Next week Tom stumbled into Lucy by the lockers…”
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!
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