2023-12-05 04:06:53 <xelxebar    > KipIngram: Yeah, the one point compactifications (Reimann circle, sphere, etc.) do let you define x/0 for non-zero x, but then you just introduce other undefined entities: ∞-∞ and ∞·0, and 0/0 remains undefined.
2023-12-05 04:08:07 <xelxebar    > The trick with wheels is that it makes multiplicitive inversion a total operation, just like negation as additive inversion is total.
2023-12-05 04:11:38 <xelxebar    > Wheels are a bit more systematic in a sense, but the reason they're called a wheel is because the one-dimensional case looks like the Reimann line but with an extra point: ⊙.
2023-12-05 13:24:57 <KipIngram   > I see - like a Riemann sphere but only for reals.
2023-12-05 13:27:35 <KipIngram   > It's never really particularly bothered me that 0 has no inverse.  It's a bit like us having a large dance floor, but there is a hole over there we might step through.  So we put a little guard rail around it, and then the rules are just "go anywhere you want, except you can cross that barrier - there's trouble on the other side."
2023-12-05 13:27:44 <KipIngram   > ugh - s/can/can't/
2023-12-05 13:28:02 <KipIngram   > Just don't go there and everything works just fine.
2023-12-05 13:29:06 <KipIngram   > And as things turn out, inablity to reach that one little part of the dance floor doesn't cause us trouble as we go about our business.
2023-12-05 13:30:10 <KipIngram   > This is a bit of a sidetrack (though an interestng one) - the main point the other day is that regardless of whether 1/0 exists or not, it's absolutely not 0.
2023-12-05 13:30:32 <KipIngram   > If it's anything at all, it's infinity.
2023-12-05 13:31:07 <KipIngram   > The rest of our discussion here is about whether "infinity" is something tangible or not.
2023-12-05 13:32:07 <KipIngram   > In the normal numerical field, infinity isn't in any way a number - it's kind of just an idea.  Riemann sphere, wheels, etc. let us treat it "a little more" like a number, but as you note still with some limitations.
2023-12-05 13:32:39 <KipIngram   > You can at least point right at it on a Riemann sphere.
2023-12-05 13:33:09 <KipIngram   > Whereas you can't in the more standard field of numbers.
2023-12-05 13:34:14 <KipIngram   > Roger Penrose does some neat stuff, where he maps the universe onto a diagram where "infinity" is at the outer edge.  Lets him paint the whole universe on a finite manageable drawing.
2023-12-05 13:36:10 <KipIngram   > This sort of mapping:
2023-12-05 13:36:13 <KipIngram   > https://imgs.search.brave.com/JWwrKTawxKPzZi6HEpZfr4N7Kq2eqf6WFU9vxhmlC00/rs:fit:860:0:0/g:ce/aHR0cHM6Ly9tLm1l/ZGlhLWFtYXpvbi5j/b20vaW1hZ2VzL0kv/NTFBaGFITlcrY0wu/anBn
2023-12-05 14:26:41 <user51      > That looks more evil than I expected :P
2023-12-05 14:27:22 <KipIngram   > :-)  Yeah.  It makes sense in a way - stuff "further away" is "more compressed," and the region near you is presented in most detail.
2023-12-05 14:28:15 <KipIngram   > Cosmologists have kind of a tough row to hoe - they have to somehow address "everything."
2023-12-05 14:29:12 <KipIngram   > I still struggle with significant parts of Penrose's work; the level of mathematics he works out is just out of my current reach.
2023-12-05 14:29:17 <KipIngram   > works "at"
2023-12-05 14:31:44 <KipIngram   > He theorizes that in the VERY far future, after the last black hole evaporates, the universe will contain no  matter at all - only photons.  And according to him that state is mathematically identical to the Big Bang state, since photons don't "register" distance or time passage.  So he says that then things will just "bang again."  No phase of contraction back to a point - just an endless cycle of Big Bangs,
2023-12-05 14:31:46 <KipIngram   > expansion, and eventual lose of all matter that repeats over and over.
2023-12-05 14:32:01 <KipIngram   > So, cyclic cosmology without any contraction phases.
2023-12-05 14:32:40 <KipIngram   > It's not a well-accepted theory, but he claims there is some supporting observational evidence.
2023-12-05 14:33:03 <KipIngram   > He calls each cycle an "aeon."
2023-12-05 14:33:46 <KipIngram   > And claims that at least in principle information could be delivered from one aeon to the next.
2023-12-05 14:34:19 <KipIngram   > If that had been done in the last aeon we'd theoretically find it in the cosmic microwave background.
2023-12-05 14:34:30 <KipIngram   > Seems like there are some good sci fi stories there.
2023-12-05 14:37:24 <KipIngram   > In the novel version of Contact, at the end after the whole story was over the chick played by Jodie Foster had moved on from SETI to looking for messages in the digits of pi.  In a modern spin that could have been looking for messages encoded in the CMB instead.  That would have seemed a little more plausible to me.  :-)
2023-12-05 14:37:39 <KipIngram   > Seems like only God could arrange a message in pi.
2023-12-05 14:38:26 <KipIngram   > I think it's pretty fascinating what they can learn studying the CMB.
2023-12-05 14:40:55 <KipIngram   > Those pictures you see of the CMB, by the way, are highly exaggerated.  The color indicates temperature, basically, but the total variation across the whole sky is really just one part in 100,000.  If you just "looked at it," it would look like an entirely flat, even glow.  They have to really stretch the data to get the images as usually shown.
2023-12-05 14:41:47 <KipIngram   > And also red and blue shifts arising from our solar system's motion in the galaxy and so on has been calculated out.
2023-12-05 14:42:57 <KipIngram   > You always read in physics that there's no "special frame of reference" which is "really" at rest, but in fact the CMB actually does define such a frame.
2023-12-05 14:43:31 <KipIngram   > "Rest" is the state that makes the CMB glow isotropic.
2023-12-05 14:49:28 <KipIngram   > Of course it's still not special in any "fundamental physics" sense.
2023-12-05 19:02:28 <KipIngram   > Wow, the Wikipedia article on the history of tokamak development is very detailed and interesting.
2023-12-05 19:14:57 <thrig       > written by nerds, for nerds
2023-12-05 19:35:13 <rendar      > #def double * 2 #end
2023-12-05 19:35:22 <rendar      > this is how you define new words in my Forth
2023-12-05 19:48:47 <KipIngram   > https://www.nature.com/articles/d41586-023-03854-1
2023-12-05 19:49:11 <KipIngram   > It's not RPN?
2023-12-05 19:49:57 <KipIngram   > #def == : and #end ==  ; is fine if it suits you better.
2023-12-05 19:50:37 <KipIngram   > ^^ 1000-bit quantum computer just announced by IBM.
2023-12-05 19:52:55 <KipIngram   > Still prone to errors, though.
2023-12-05 21:09:43 <KipIngram   > Toying with the idea of making a fuel cell.
2023-12-05 21:09:51 <KipIngram   > Just for the education.
2023-12-05 22:04:59 <KipIngram   > This is pretty interesting material:
2023-12-05 22:05:02 <KipIngram   > https://fusor.net/files/Ligon-QED-IE.pdf
2023-12-05 22:05:18 <KipIngram   > I had no idea such work had been done at the low end.
2023-12-05 22:05:35 <KipIngram   > Apparently you can do fusion in your garage; the problem is that it's way below breakeven.
2023-12-05 22:56:57 <zelgomer    > i'm so stupid
2023-12-05 22:57:36 <zelgomer    > create actions 8 cells allot  ... :noname  ... ;  actions !  :noname  ... ;  actions cell+ !  ( and so on )
2023-12-05 22:57:56 <zelgomer    > ah, damn, nevermind. it does have to be that way
2023-12-05 22:58:23 <zelgomer    > i was going to say it's real ugly and i only just realized i can use  create actions  :noname .. ; ,  :noname .. ; ,
2023-12-05 22:58:47 <zelgomer    > but turns out i can because i still write junk header info for :nonames. dang
2023-12-05 22:58:54 <zelgomer    > s/can/can't
2023-12-05 22:58:59 <zelgomer    > i should fix that in v2
2023-12-05 23:05:38 <zelgomer    > if you have a word that adds bit fields to a  variable mask   would you call it  >mask  or  mask!  or  >mask!