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iLate reply, but the slicker bit is going in more fully. The appeal of the NSA approach here is axiomatizing it which helps people understand because people already know what numbers are, so 'inf big' is much less of a stretch than going the usual crazy inference depth math has.
This really benefits from a picture. Calling something “a nonstandard number” doesn’t really convey anything about them and a better name I’ll use is “infinitely big”, because they are.
< makes sense because the 2 chains are finite numbers and infinitely big numbers and an infinitely big number is bigger than any finite one because it’s , well, infinite. I can elaborate more technically, but I think trying to develop some numeracy for infinite numbers is a lot like learning about negatives and rationals and complex numbers. Just play with some expressions and get used to them. then look at the more technical treatment even if you have the ability to read it. Someone gave that example with a flat list but I think and feel that tapping into one’s existing NUMBER (and not list) sense is very powerful since it’s the first math we learn and the only one people use every single day.
"This" is the broken duality phenomenon?
Through stone duality. What about them in particular?
thanks, i think. how'd you find the content?
I think there’s an implicit element of scale or one offness. For buying milk you have multiple samples as to good price. Even if any is contrived, the bulk still capture something real
reminded me of https://en.wikipedia.org/wiki/Winner%27s_curse
lol laffy taffy is too real banana sucks
Train skill of noticing tension and focus on it. Tends to dissolve. No that's not so satisfying but it works. Standing desk can help but it's just not that comfortable for most.
that the functional analysis is mildly helpful for understanding the problem, but the focus of the field doesn't seem to be on anything helpful. VC dimension is the usual thing to poke fun at, but a lot of the work on regularization is also meh
Dissection tonight at Merritt College in Oakland, building S202. 5:30-9, you can pay by paypal.
UCSF willed body program, on contract to Merritt College.
(Something that came up yesterday, parens give the particular case.)
Have you spent a lot of time on a skill without a cap? (like math)?
Have you paid money for it? (math tutoring)
How much?
How much have you paid towards a complementary unbounded skill (managing people, voice coaching).
So yeah, between learning another hour of math and a voice coach, both at $~80/hour, is the marginal util of voice coach[1] way lower[2]?.
- ^
Or whatever soft skill you would benefit from but don't do.
- ^
way because estimates of utility are fuzzy. [don't lie to yourself.](https://www.goodreads.com/quotes/302239-above-all-do-not-lie-to-yourself-a-man-who)
L1 and L infinity norm in another way:
see infinity as an unlimited integer N. The max property of the infinity norm
will still hold.
I still wonder about the parity prediction these days. I feel like there's something there
Except that you can have a thread just for conversations. It subsumes the chat model.
The point is that such a distribution (uniform on countable infinite set like naturals), is not internal, and therefore external. it'll depend on the specific ultrafilter used under the hood.
for how to use it, see either alain roberts or sylvia wenmackers
fact: there is no set of all finite sets
One way size goes seems to be:
Limited/finite, actual infinity (countable), potential infinity (uncountable/hyperfinite/compact regions).
On limited and uncountable inputs, we can define a uniform distribution naturally.
A uniform distribution on a countable set, there's no natural way to do that. So in a way, they're "bigger".
the nameless rationalist virtue (void)
Extremely based.
Related: Ends of groups: a nonstandard perspective, Journal of Logic and Analysis, Volume 3:7 (2011), 1-28.
Ends are havens in pursuit games
Differential games lend themselves to a hyperfinite description. You can even have turns. Each player takes an infinitesimal move, then the other goes. A hyperdiscrete approach.
Observing your opponent becomes really important, like in a fight, soccer, or a relationship 😶. I have the intuition that the OODA loop falls out of this.
There's a classic game here where you run from a lion, and the optimum is running along a harmonic spiral since it's infinitely long. What would that look like under this?
A while ago, I saw Dan Savage's film festival. As an intense art student ate 1000 condoms, a thought flashed. Many gears, all ticking. Click. Click. Clock.
And it hit me: every finite commutative group is a product of cyclic groups of prime power order, just like a prime factorization.
I still have no idea how that came in that context.
I was thinking the one corresponding to a unit circle, just the ordinary dot product.
Canon is probably the wrong word in a mathy context.
Also yes the infinitesimal neighborhood of the identity.
Done 🙏
https://link.springer.com/book/10.1007/978-3-642-33149-7
Also includes Feynman path integral and a few other things. Note that you don't even need the full nonstandard theory.
https://www.sciencedirect.com/science/article/pii/S0049237X08715507
On any finite dim space we have a canon inner product by taking the positive definite one.
Monad is a synonym for infinitesimal neighborhood, common on the literature. Not the category theory monad.
Also hermeneutic lmfao
What can 20k USD buy, including projects?
Edit: I live in Berkeley.
I'll just say for now. Basically wrapping up "is all this an elaborate simulation designed to convince me that pi = 12"
handy trick inspired by compactification: we can work with completed structures by adding endpoints and taking them away.
example: for a lattice, we can adjoin 0 and 1 as min/max elements by defining a structure where the sentences and are true for all in the original structure, then do what we want, then delete 0 and 1.
cool goldbring paper: http://philsci-archive.pitt.edu/19419/1/nonstandard_everett.pdf
handy hyperreal trick
take "the hilbert space" talked about in QFT. Set it to where H is hyperfinite. Have fun. "Compact operators" fall out, and everything finitary is in there, but the whole thing isn't finite
.
reading https://ncatlab.org/nlab/show/formal+disk convinced me that there's something to my feeling that nonstandard analysis is similar to algebraic geometry.
formal disk ~ infinitesimal neighborhood/halo of a point ~ formal spectrum of power series, which extends prime spectra, one of the main concepts of algebraic geometry. any help here appreciated
Was being deliberately inaccurate here. Hard does mean more than a limited multiplier. Sudden means that there's an appreciable change over an infinitesimal variation aka discontinuous.
Lookup overflow, underflow, and "principle of permanence" in Goldblatt for why I'd do that. Also called overspill and underspill. The basic idea is "as above, so below" except this link is 2 way. Say some internal function has all infinitesimals in its range. Then it must have non infinitesimals too, since the set of all infinitesimals is known to be external, and images of internal functions over internal sets are internal. This is an example of overspill. Infinitesimal behavior has spilled over into the appreciable domain.
Reread this and this is awesome: I didn't think of the case of multiple bars at all. As for the surreal stuff, I've read about them and while the lexicographic ordering is nice, the lack of transfer principle hurts. Are you in the bay?
The logic of paradox, or https://philarchive.org/archive/POSBTO-2
Look up "Sylvia wenmackers numerosity"
Think of diffusion as a micro random walk. A hyperfinite number of infinitesimal steps, sampled from a discrete set of vectors.
This is inspired by the old 'trade _ for money' posts.
I think the Anova Oven should be the default rationalist oven. It is $500, but on this community isn't usually hurting for cash.
That $500 gets you something so beyond a normal oven it's basically a different tool. It's better thought of as a largish box whose temperature you control. To see this, make scrambled eggs in it. They have a recipe in their app.
It can reliably control temperature all the way down to 77 F (25 C), making it capable of cooking almost any kind of meal. It's programmable, so longer recipes are simple to set up.
Reheating food (and making a lot) becomes trivial, and unlike a microwave there's no problems with ice staying frozen. Reheating to 150F makes almost all leftovers taste fresh.
reading https://ncatlab.org/nlab/show/formal+disk convinced me that there's something to my feeling that nonstandard analysis is similar to algebraic geometry.
formal disk ~ infinitesimal neighborhood/halo of a point ~ formal spectrum of power series, which extends prime spectra, one of the main concepts of algebraic geometry. maybe i can skip the category theory and just write out some polynomials
late 14c., ethimolegia "facts of the origin and development of a word," from Old French etimologie, ethimologie (14c., Modern French étymologie), from Latin etymologia, from Greek etymologia "analysis of a word to find its true origin," properly "study of the true sense (of a word)," with -logia "study of, a speaking of" (see -logy) + etymon "true sense, original meaning," neuter of etymos "true, real, actual," related to eteos "true," which perhaps is cognate with Sanskrit satyah, Gothic sunjis, Old English soð "true," from a PIE *set- "be stable."
mathy interpretation of the bit about truth: (longer ~ chains are weaker) true ~~ stable ~~~ a starting point for reasoning ~ point ~ .
Ty for forum tip
models let us conduct words, and soonish pictures
chatgpt is very micromanageable too
(it = chatgpt) (ask it to rewrite this post to active tense and written in a way that's pleasant to read) (read this post like pseudocode^2, with a lot of thought about general and particular, and the fundamental ncatlab dialectic)
[wow this really may make dreamposting possible. magic =).]
ask it to consider the morality of whatever you think of
help me pls uwu.
ask it to break it down into a plan for you.
to make that plan as easy as possible
have it generate api code (if the docs were available <2022)
ask it to check its work to print out a (informal) proof or line of reasoning or whatever
tell it to think about lojban and output in lojban and then in english. make it elaborate
have it explain in 4chan style, or whatever
ask it to write out general and particular in its line of reasoning
ask it to explain "words ~ concepts ~ region of space"
ask it to rewrite bits of Dune to not drag so much
it can expand and contract text by simplification and elaboration.
reasoning is most of what you want to give it, and the particulars
try using chatgpt to optimize life. they have an api too.
try giving it really specific instructions and general stuff, then the particulars.
Example of hyperfinite quantity: number of sides of a circle
lawyer ~ social programmer
precedent ~ import 'precedent'
judge ~ debugger
jury ~ the actual, buggy thing that runs in the very end
jargon ~ lang syntax
Thanks =). Any way to access fresh cadavers? I doubt I’ll be allowed to do surgery anytime soon.