The important feature of Hilbert's example is not the hotel, or the guests, but the strange consequence of Cantor's method for 'counting' an infinite collection of objects. William Dunham's Journey through genius does an excellent job with Cantor in his final two chapters. I'm paraphrasing him.
Suppose you want to know if you have more than 5 raspberries. You could count them, or you could stick them on the ends of your fingers. If you have berries left over, there were more than five. If all the berries fit all the fingers, you have put your fingers in a 1-to-1 correspondence with the berries, and concluded that the numbers of each are the same. That's how small children count, and Cantor's genius was to extend this idea to sets of infinite objects.
If you can find a 1-to-1 correspondence between the counting numbers (1,2,3,...) and some other set of objects, then the size of the two sets must be equal (in the business, size of sets is called the 'cardinality'). It is traditional to denote the counting numbers by 'n'.. Hilberts 'paradox' arises from Cantors claim that there are as many counting numbers as even numbers. The correspondence is n->2n. For every counting number, I can double it to find every even number. That's weird.
You can just as easily show that there are as many odd numbers as counting numbers. The scheme is more complicated, but you can also find a 1-to-1 correspondence between the counting numbers and all the fractions between 0 and 1. It seems like the counting numbers can count everything! But that's not the whole story.
The big shock is that there are more numbers between 0 and 1 than counting numbers. That is Cantors 'nondenumerability of the continuum'. I highly recommend Dunhams book. The proof of the nondeumerabilty theorem is so beautiful and accessible (like accessible to a ten year old).
Babe, it's not 'rotting'. It's 'getting funky' like blue cheese does. 'Look at me, getting funky while the laundry piles up.' That sounds terrific, like Bootsy Collins with his hands full.
I've got the previous version, and it's about 7 years old. But the power is good (I would definitely get the larger model if that is a concern). Battery is okay; maybe 30-45 mins full charge, and definitely more power right after charging. But I think that's probably my old girl showing her age.
Smitten kitchen is fantastic. Recipe are all great (any that I have tried), photos are amazing, and Deb Perelman is delightful. But no rss feed as far as I can tell.
Have you tried the death stranding series? I just finished 2 yesterday. It was fantastic. In both, you can tailor your experience - skip cut scenes, drop difficulty to 'story' for frustrating fights, etc. But those games tell a story in a way only video games can. And all the little flourishes that emotionally connect you to your character, like rocking the controller to sooth the baby sealed in your chest pod, are so charming and affecting.
I thought Instant physics by Rothman was a good semi-popular overview. It's a good birds-eye-view of undergraduate physics.
MIT has an incredible archive of open course ware. If there are specific topics you want to pursue in-depth, that is a great resource for lectures, practice problems, and demonstration videos.
For math, I think 3blue1brown does an incredible job. Here is his take on the essence of calculus. If you prefer textbooks, there are many open-source options. MIT is a good source of open lectures, texts, and problem sets.
It is pretty tough to follow the derivation, but the vee in the first term of eq 22 (friction force integral) is the plate velocity (see eq 5). Is that the 'in terms of velocity' you had in mind?
It's buried in advanced settings. Preferences>Settings>I am an advanced user, then when you open the ublock panel on a website, you can disable 3rd party frames and scripts. As Oberon said, adding 'accounts.google.com/gsi/client' to My filters blocks google specifically.
Twine is a tool for writing nonlinear, choose-your-own-adventure type stories. Outputs to html, so it super-portable. It might fit your needs, depending upon what you had in mind for game play outside the dialog. Still might be useful for story-boarding, and mapping out the narrative.
I got a lot out of Saundra Yancy McGuire's books "teach students how to learn" and "teach yourself how to learn". If your library has them, that might be the way to go. Not sure they're meaty enough to justify a purchase.
But that said, her illustration of Bloom's taxonomy using the story of Goldilocks could provide a week's-worth of lessons.
Thanks!
Lovely! Are the veins felted, too, or stitched? I think this is how I'm spending my Saturday.
Apes of the state
The important feature of Hilbert's example is not the hotel, or the guests, but the strange consequence of Cantor's method for 'counting' an infinite collection of objects. William Dunham's Journey through genius does an excellent job with Cantor in his final two chapters. I'm paraphrasing him.
Suppose you want to know if you have more than 5 raspberries. You could count them, or you could stick them on the ends of your fingers. If you have berries left over, there were more than five. If all the berries fit all the fingers, you have put your fingers in a 1-to-1 correspondence with the berries, and concluded that the numbers of each are the same. That's how small children count, and Cantor's genius was to extend this idea to sets of infinite objects.
If you can find a 1-to-1 correspondence between the counting numbers (1,2,3,...) and some other set of objects, then the size of the two sets must be equal (in the business, size of sets is called the 'cardinality'). It is traditional to denote the counting numbers by 'n'.. Hilberts 'paradox' arises from Cantors claim that there are as many counting numbers as even numbers. The correspondence is n->2n. For every counting number, I can double it to find every even number. That's weird.
You can just as easily show that there are as many odd numbers as counting numbers. The scheme is more complicated, but you can also find a 1-to-1 correspondence between the counting numbers and all the fractions between 0 and 1. It seems like the counting numbers can count everything! But that's not the whole story. The big shock is that there are more numbers between 0 and 1 than counting numbers. That is Cantors 'nondenumerability of the continuum'. I highly recommend Dunhams book. The proof of the nondeumerabilty theorem is so beautiful and accessible (like accessible to a ten year old).
Babe, it's not 'rotting'. It's 'getting funky' like blue cheese does. 'Look at me, getting funky while the laundry piles up.' That sounds terrific, like Bootsy Collins with his hands full.
I was also super-curious. It looks amazing. Took some sleuthing, but it is Kinusaiga. Double-sided tape on foam board.
Rivers and tides is an amazing 2001 documentary of his work.
I've got the previous version, and it's about 7 years old. But the power is good (I would definitely get the larger model if that is a concern). Battery is okay; maybe 30-45 mins full charge, and definitely more power right after charging. But I think that's probably my old girl showing her age.
I love this one, but everything by Lelo is so beautiful.
Smitten kitchen is fantastic. Recipe are all great (any that I have tried), photos are amazing, and Deb Perelman is delightful. But no rss feed as far as I can tell.
Have you tried the death stranding series? I just finished 2 yesterday. It was fantastic. In both, you can tailor your experience - skip cut scenes, drop difficulty to 'story' for frustrating fights, etc. But those games tell a story in a way only video games can. And all the little flourishes that emotionally connect you to your character, like rocking the controller to sooth the baby sealed in your chest pod, are so charming and affecting.
If 'the curse' looks good to you, Rachel Deerling's Anathema is another take.
Alan Moore's The Curse is in that direction.
I thought Instant physics by Rothman was a good semi-popular overview. It's a good birds-eye-view of undergraduate physics.
MIT has an incredible archive of open course ware. If there are specific topics you want to pursue in-depth, that is a great resource for lectures, practice problems, and demonstration videos.
Glenn Gould? When he's holding forth, he seems like a Nixon impersonator doing college radio.
For math, I think 3blue1brown does an incredible job. Here is his take on the essence of calculus. If you prefer textbooks, there are many open-source options. MIT is a good source of open lectures, texts, and problem sets.
For general expert suggestions about a variety of subjects, I like five books, for example here are some suggested books on linguistics, religious studies, international relations, and art theory.
It is pretty tough to follow the derivation, but the vee in the first term of eq 22 (friction force integral) is the plate velocity (see eq 5). Is that the 'in terms of velocity' you had in mind?
It's buried in advanced settings. Preferences>Settings>I am an advanced user, then when you open the ublock panel on a website, you can disable 3rd party frames and scripts. As Oberon said, adding 'accounts.google.com/gsi/client' to My filters blocks google specifically.
Twine is a tool for writing nonlinear, choose-your-own-adventure type stories. Outputs to html, so it super-portable. It might fit your needs, depending upon what you had in mind for game play outside the dialog. Still might be useful for story-boarding, and mapping out the narrative.
I got a lot out of Saundra Yancy McGuire's books "teach students how to learn" and "teach yourself how to learn". If your library has them, that might be the way to go. Not sure they're meaty enough to justify a purchase.
But that said, her illustration of Bloom's taxonomy using the story of Goldilocks could provide a week's-worth of lessons.