I remember seeing (x+1) ^ 2 in math class and thinking it would just be x^2 + 1. But it’s actually x ^2 + 2x +1.
Okay fine, you have to multiply out each term by each term. The x * x, the x * 1, the other x * the other 1 and 1 *1.
I just took this for granted, like it was just how you’re supposed to do it via the formula.
But if you look at it on a piece of graph paper, say draw a 2 x 2 square, and say, if x = 2, what is (x +1) ^ 2?
Well you keep the x ^ 2 (the box with area 4), and you add 2x (2) to the top of the box and 2x to the side of the box, but then there’s one small square missing, so you add that, and now you have a 3 x 3 box.
And you do it again to get a 4 x 4 square, just add another 3 on top, 3 on the side, and fill in the one that’s missing.
And you can keep going, and the formula makes perfect sense.
And you realize to go from x ^ 2 to (x + 1) ^ 2, you can always just add x + (x+1) to x ^2. Or 2x +1 to x ^2.
That’s why a 4 x 4 square = 16. And a 5 x 5 square = 16 + (2 * 4) +1. And a 6 x 6 square = 25 plus (2 * 5) + 1. Etc.
So if you want to calculate 101 squared in your head, you can just do 100^2 = 10K, plus 100, plus 101 - 10,201. And 101 ^ 2 = 10,201 plus 101 plus 102 - 10,404. Etc.
Maybe this is obvious to some people, but it blew my mind how you can do this easily in your head.
I spent the entire seven hour flight battling a tough Sudoku. I even spilled water on it at one point and had to let it dry. I defeated it 40 minutes before we landed. I felt as though the fate of me and my fellow passengers depended on my completing it.
They would never allow this in a million years for obvious reasons. People would just stop paying for 95 percent of things. Might as well just end income tax entirely at that point.
View quoted note →Ate some yogurt at my brother’s house, upscale fancy brand. Tasted a little off, but figured that’s because it’s the fancy stuff. Then I noticed the expiration date was 8/14, had been open in the fridge for two months!
No mold though. Deciding whether to worry about this or not.
Waiting at the gate some millennial libs were talking animatedly about politics. The theme was their magnanimity in not de-friending people who had abhorrent views, you know like being against “gender affirming care.”
It was this nervous attempt to find uncomfortable consensus amongst themselves for how to deal with dissenting views.
It actually took some restraint for me not to say something along the lines of: “You people don’t know ANYTHING about anything.” Just lost souls grasping at phantoms.
Really enjoyed the night time cab ride from JFK to the city. Sikh cabbie driving the minivan like a maniac, making great time, like Virgil leading me through the various underworlds on the outskirts of town.
Decrepit motels with only one letter of the neon sign half blinking, places no doubt where overdoses and rapes are commonplace. Then the run down houses with full views of the highway, various stretches of housing projects, apartments blue-lit by TV screens.
Through the midtown tunnel and I’m in a futuristic glass and steel world, superimposed on the old beautiful city with upscale bistros, bars and galleries. Time travel from old Europe.
Driver drops me off at my destination, tip him well, thank him for the excellent, speedy driving. Could tell he took pride in risking our lives so skillfully and appreciated the sincere compliment.
90 YO uncle having some cognitive issues,sister in law arranges to have a caretaker swing by his place to help him out. But when she knocks on the door, he refuses to let her in, tells my brother afterward he wants someone younger and more attractive.
People at airports are increasingly unhealthy looking, and many of them seem insane.
Feel like something’s cracking which is why there’s a sell-off. People need to raise dollars desperately.
Had an international flight to catch today at 5. Get a text from the airline saying due to the new immigration system being put in, get to the outgoing immigration line 3 hours early. WTF?
So I tell my wife to drive me early, she thinks I’m crazy. She always does it last minute, I don’t care about being stuck at the airport, just don’t want to miss my flight.
Anyway, we leave an hour and a half earlier than even I had planned, she drops me off. I was literally the ONLY one in the immigration line. I walked right to the front, got to the “gate” three hours early. I put “gate” on quotes because I won’t have a gate for another hour.
Expect some shitposts, I got nothing better to do.
Seems like SSRIs, birth control and the mRNA have done a lot of damage to a lot of people.
You thought it was Uptober, but it was really Choptober
Think I discovered at age 54 I have a learning disability. I’m *differently abled* LOL.
Was talking with my mom who told me she had a learning disability (she’s 80 next week), I never knew. She said she has trouble reading. I said you can read! She said yeah, but slowly and often she has to read sentences three times to understand them.
I thought about it, and I’m similar though WAY better adapted than she is. I can read novels quickly, but new subjects, especially tech ones make my mind glaze over. I just can’t get it, until I ask a lot of really basic dumb questions and it finally clicks.
I was good at math as a kid, but had trouble with multi-variable calculus in college. I always chalked it up to excessive partying, but I did study in the end, killed myself to get an 80 on the final exam and a C- in the course overall.
I get this same feeling with tech, coding, nostr features, etc. It takes me a long time to get it, but oddly, once I get it, I really get it.
I have to understand from first principles and build the entire edifice on top, otherwise I am lost. I don’t do mimetic learning well, I have a hard time picking up languages, for example. I can’t “fake it till I make it.” I can’t fake it at all. I either know it or I don’t.
Paradoxically this has given me a super-power of sorts — I can explain things I understand very clearly because I am explaining them to my retarded self. I assume you are not taking leaps, and literally spell it out from first principles step by step. There are few to none elisions in the explanation and even people who don’t have this issue can get something out of them.
It also informs my belief that anyone no matter how retarded (within limits) can understand ANYTHING that anyone no matter how intelligent can understand, provided the building blocks are presented clearly enough and broken down into digestible enough pieces.
Anyway, just a bizarre thing to discover at this age, but it explains a lot.
The future of media has to be you type in what you want to see, pay for it and the creators sort out the payment on the backend. No more myraid subscriptions to streaming services. Just pick the content, pay the cost and let them figure it out.
At first it will be credit cards, but eventually just sats. Load up your TV-browser-wallet with sats, spend and refill as needed.
Trusted curators will emerge, people who take half a percent for you to use their lists, deal with the problem of discovery.
Pirating will happen, but they could release free ad-full and paid ad-free versions, so anyone who doesn’t want to pay can watch the ads, and that would limit it because why bother with the pirated version if you can get it anyway.
Also every purchase could be an NFT (finally a use case!) so you’d know you got a non-pirated paid one.
Would be a privacy issue, but no problem, if you spin up an anon nostr account, load it with sats and buy your content with that one.
The Mag 7 will never again crash in dollar terms. If they start to, the government will just print and prop them up. But they will crash relative to bitcoin. Once it’s obvious people’s ATH stocks have lost purchasing power, the unit of account will change implicitly. It’s already happening when people note the ATH in bitcoin isn’t an ATH vs gold. The unit of account is already slipping.
@hal how many active users (defined by five posts of more than 100 words per week) are on nostr?