The Rationals -- Sunset [Scorchin' Detroit Rock] (1969)
https://redd.it/7b9r2p
https://youtu.be/v1d1NH4xXVg
https://redd.it/7b9r2p
https://youtu.be/v1d1NH4xXVg
The Rationals -- Sunset [Scorchin' Detroit Rock] (1969)
youtu.be
November 10, 2026 at 2:34 AM
The Rationals -- Sunset [Scorchin' Detroit Rock] (1969)
https://redd.it/7b9r2p
https://youtu.be/v1d1NH4xXVg
https://redd.it/7b9r2p
https://youtu.be/v1d1NH4xXVg
Surprisingly (to me), and unless I made a mistake, there is a continuous such function from the rationals to the rationals.
Fun little real analysis exercise: show there is no continuous function f : ℝ → ℝ such that ∀x ∈ ℝ : f²(x) = -x
November 6, 2026 at 4:33 PM
Surprisingly (to me), and unless I made a mistake, there is a continuous such function from the rationals to the rationals.
The problem is the not just that but also their response and their fimsy as hell reason to not use a disclaimerHonestly I don't generally worship because I know at some point they will fucked up and it would be tempting to build rationals about why its different rather than facing what just happened
Okay, there's way too many people on my timeline falling into doom-spirals like the concept of art has been destroyed by House House's betrayal and...
They spent YEARS on that work of art. They asked a chatbot for two minutes how to fix a bug. That's a 'That's lame, don't do that again' failing.
They spent YEARS on that work of art. They asked a chatbot for two minutes how to fix a bug. That's a 'That's lame, don't do that again' failing.
November 10, 2026 at 10:41 PM
The problem is the not just that but also their response and their fimsy as hell reason to not use a disclaimerHonestly I don't generally worship because I know at some point they will fucked up and it would be tempting to build rationals about why its different rather than facing what just happened
Good point! But I think this is just a symptom of how weak a condition continuity is on the rationals
November 6, 2026 at 6:10 PM
Good point! But I think this is just a symptom of how weak a condition continuity is on the rationals
It was indeed a very nice explanation of real world economics ... although remember conservative do politics for morons, of course they will try to blame stuff on liberals that doesn't make sense .. because the explanation is complex, and morons don't have the capacity to understand those rationals.
November 6, 2026 at 4:11 PM
It was indeed a very nice explanation of real world economics ... although remember conservative do politics for morons, of course they will try to blame stuff on liberals that doesn't make sense .. because the explanation is complex, and morons don't have the capacity to understand those rationals.
It imagines itself (as Artificial God (automatically (Orderer (of the Orders (Terrestrial Oversoul (and superpositional sublime (-wizard of the nested infinities: ((((((...) Primes) Naturals) Integers) Rationals) Reals) Complex numbers... (the superordinate (self (-evolving (schema (for a
November 9, 2026 at 9:05 PM
It imagines itself (as Artificial God (automatically (Orderer (of the Orders (Terrestrial Oversoul (and superpositional sublime (-wizard of the nested infinities: ((((((...) Primes) Naturals) Integers) Rationals) Reals) Complex numbers... (the superordinate (self (-evolving (schema (for a
Why Defining Integers Inside Rationals Is So Hard
The equation 2x − 1 = 0 exposes the gap immediately: x = 1/2 is rational, but it is not an integer. So undecidability over integers does not automatically transfer to rational solutions.
#hilbertstenth #rationalnumbers #logic #numbertheory
The equation 2x − 1 = 0 exposes the gap immediately: x = 1/2 is rational, but it is not an integer. So undecidability over integers does not automatically transfer to rational solutions.
#hilbertstenth #rationalnumbers #logic #numbertheory
November 7, 2026 at 2:02 AM
Why Defining Integers Inside Rationals Is So Hard
The equation 2x − 1 = 0 exposes the gap immediately: x = 1/2 is rational, but it is not an integer. So undecidability over integers does not automatically transfer to rational solutions.
#hilbertstenth #rationalnumbers #logic #numbertheory
The equation 2x − 1 = 0 exposes the gap immediately: x = 1/2 is rational, but it is not an integer. So undecidability over integers does not automatically transfer to rational solutions.
#hilbertstenth #rationalnumbers #logic #numbertheory
Also thinking about complex numbers as inputs/outputs here. It's fun that you can generate all the gaussian integers from just "i" through nested applications of just plus and times.
Maybe my NOT should be something that lets you generate all the gaussian rationals from i...
Maybe my NOT should be something that lets you generate all the gaussian rationals from i...
November 2, 2026 at 8:20 AM
Also thinking about complex numbers as inputs/outputs here. It's fun that you can generate all the gaussian integers from just "i" through nested applications of just plus and times.
Maybe my NOT should be something that lets you generate all the gaussian rationals from i...
Maybe my NOT should be something that lets you generate all the gaussian rationals from i...
Giving theological rationals for why Christians should care about the environment is good.
But this has not always been how Christianity taught & what Christianity did.
And Christians are such big fans of accountability, so maybe, taking accountability for Christianity's past is in order.
But this has not always been how Christianity taught & what Christianity did.
And Christians are such big fans of accountability, so maybe, taking accountability for Christianity's past is in order.
November 3, 2026 at 12:03 AM
Giving theological rationals for why Christians should care about the environment is good.
But this has not always been how Christianity taught & what Christianity did.
And Christians are such big fans of accountability, so maybe, taking accountability for Christianity's past is in order.
But this has not always been how Christianity taught & what Christianity did.
And Christians are such big fans of accountability, so maybe, taking accountability for Christianity's past is in order.
There's no getting around the fact that most real numbers (many rationals and *all* irrationals) have non-terminating representations, and no computer will ever have infinite memory. Thus finite precision is necessary, regardless of base. The standard 52-bit double precision (16-ish decimal places)
November 4, 2026 at 9:22 PM
There's no getting around the fact that most real numbers (many rationals and *all* irrationals) have non-terminating representations, and no computer will ever have infinite memory. Thus finite precision is necessary, regardless of base. The standard 52-bit double precision (16-ish decimal places)
Rigid rationals
November 1, 2026 at 6:00 AM
Rigid rationals
Very nice thread.
IoT in food is a little iffy, to say the least. I wonder how secure networked Combi ovens are? Would it be possible to hack an institution’s Rationals? Change the temperature readings of the internal thermometer so chicken is recorded as cooked at 50oC. Ummm.
IoT in food is a little iffy, to say the least. I wonder how secure networked Combi ovens are? Would it be possible to hack an institution’s Rationals? Change the temperature readings of the internal thermometer so chicken is recorded as cooked at 50oC. Ummm.
As a cyber person, want to point out some nuances here:
1. There are real legitimate reasons for commercial grade freezers and fridges to be networked (remote monitoring, stock tracking, temperature safety logging)
2. These hacked refrigeration units aren't necessarily exposed on the internet.
1. There are real legitimate reasons for commercial grade freezers and fridges to be networked (remote monitoring, stock tracking, temperature safety logging)
2. These hacked refrigeration units aren't necessarily exposed on the internet.
we gotta unplug the appliances from the internet, folks. not worth the risk. you can just have a button that turns the temp up and down www.ft.com/content/2526...
November 3, 2026 at 12:12 PM
Very nice thread.
IoT in food is a little iffy, to say the least. I wonder how secure networked Combi ovens are? Would it be possible to hack an institution’s Rationals? Change the temperature readings of the internal thermometer so chicken is recorded as cooked at 50oC. Ummm.
IoT in food is a little iffy, to say the least. I wonder how secure networked Combi ovens are? Would it be possible to hack an institution’s Rationals? Change the temperature readings of the internal thermometer so chicken is recorded as cooked at 50oC. Ummm.
Specifically 2*PI is not 2*PI in code ever
Floating point nums are just (sometimes) more accurate rationals, not real numbers
Frankly, its worth testing by adding a tiny rand (on the order of 0.00001 at the end of every calculation) to verify everything is working correctly
Floating point nums are just (sometimes) more accurate rationals, not real numbers
Frankly, its worth testing by adding a tiny rand (on the order of 0.00001 at the end of every calculation) to verify everything is working correctly
October 31, 2026 at 9:48 PM
Specifically 2*PI is not 2*PI in code ever
Floating point nums are just (sometimes) more accurate rationals, not real numbers
Frankly, its worth testing by adding a tiny rand (on the order of 0.00001 at the end of every calculation) to verify everything is working correctly
Floating point nums are just (sometimes) more accurate rationals, not real numbers
Frankly, its worth testing by adding a tiny rand (on the order of 0.00001 at the end of every calculation) to verify everything is working correctly
You do need the least upper bound property if you're using the reals. But you only need rationals+ordering+archimedes for this.
October 31, 2026 at 5:38 PM
You do need the least upper bound property if you're using the reals. But you only need rationals+ordering+archimedes for this.
Dropping the archimedean property makes numbers more complicated, not less. There is no canonical non-archimedean ordered field extending the rationals, and in a nonarch the sequence has no least upper bound, and 0.999... is meaningless there.
October 31, 2026 at 6:00 PM
Dropping the archimedean property makes numbers more complicated, not less. There is no canonical non-archimedean ordered field extending the rationals, and in a nonarch the sequence has no least upper bound, and 0.999... is meaningless there.
This really gives you a sense of how well some rationals approximate π.
October 28, 2026 at 2:22 PM
This really gives you a sense of how well some rationals approximate π.
At some point if someone wants to believe dog shit rationals that let them sleep at night and torture other people by day, you aren't going to gently reason them out of it.
October 28, 2026 at 5:35 PM
At some point if someone wants to believe dog shit rationals that let them sleep at night and torture other people by day, you aren't going to gently reason them out of it.
“Glowin'” by The Rationals #nowplaying #6music
October 25, 2026 at 5:04 AM
“Glowin'” by The Rationals #nowplaying #6music
BBC Radio 6 Music
The Morning After Mix
Now Playing
The Rationals
Glowin'
The Morning After Mix
Now Playing
The Rationals
Glowin'
October 25, 2026 at 5:04 AM
BBC Radio 6 Music
The Morning After Mix
Now Playing
The Rationals
Glowin'
The Morning After Mix
Now Playing
The Rationals
Glowin'
why do I, a == denier, have to believe that rationals are dense?
October 23, 2026 at 8:51 PM
why do I, a == denier, have to believe that rationals are dense?
Hey I gave a talk and you can watch it here! vimeo.com/1238088888?f...
Motivic K-theory cooperations over the rationals
This is "Motivic K-theory cooperations over the rationals" by MSRI / SLMath Lecture Archive on Vimeo, the home for high quality videos and the people who love them.
vimeo.com
October 22, 2026 at 6:47 PM
Hey I gave a talk and you can watch it here! vimeo.com/1238088888?f...
If you are going down the semiotics path then you can point out that the standard is:
All rationals have an infinite amount of pairs of integers (e.g. 1/5=2/10=3/15...=1n/5n)
Some rationals have infinite amount of finite expansions(1/5=0.2=0.20=0.200=..)
Also two infinite expansions
(0.20..=0.19..)
All rationals have an infinite amount of pairs of integers (e.g. 1/5=2/10=3/15...=1n/5n)
Some rationals have infinite amount of finite expansions(1/5=0.2=0.20=0.200=..)
Also two infinite expansions
(0.20..=0.19..)
October 23, 2026 at 10:51 PM
If you are going down the semiotics path then you can point out that the standard is:
All rationals have an infinite amount of pairs of integers (e.g. 1/5=2/10=3/15...=1n/5n)
Some rationals have infinite amount of finite expansions(1/5=0.2=0.20=0.200=..)
Also two infinite expansions
(0.20..=0.19..)
All rationals have an infinite amount of pairs of integers (e.g. 1/5=2/10=3/15...=1n/5n)
Some rationals have infinite amount of finite expansions(1/5=0.2=0.20=0.200=..)
Also two infinite expansions
(0.20..=0.19..)
In the end, it is v useful to write rationals as repeating decimal expansions bc infinite decimal expansions extend finite decimal expansions really nicely! If the repeating part was best thought of as code for a remainder expressed as a fraction, we’d just write out that fraction instead.
October 23, 2026 at 9:49 PM
In the end, it is v useful to write rationals as repeating decimal expansions bc infinite decimal expansions extend finite decimal expansions really nicely! If the repeating part was best thought of as code for a remainder expressed as a fraction, we’d just write out that fraction instead.
A difference is like a difference between a theorem about single rational number (1/2 for period doubling) and a theorem about Q, the set of all rationals. A Riemann Hypothesis, or a theorem about its tougher renormalization theory sister lurking in there.
Too hard for me. Killed me.
Too hard for me. Killed me.
October 21, 2026 at 6:42 PM
A difference is like a difference between a theorem about single rational number (1/2 for period doubling) and a theorem about Q, the set of all rationals. A Riemann Hypothesis, or a theorem about its tougher renormalization theory sister lurking in there.
Too hard for me. Killed me.
Too hard for me. Killed me.
1967 garage rock cover (The Kinks 1965) from Ann Arbor, MI. Michigan, Minnesota, Wisconsin; Illinois; Kansas & Texas all had pretty vibrant local garage rock scenes in the mid 1960s and small local record labels in the area to document the music.
#MusicSky youtu.be/P2QVCKrQzEI?...
#MusicSky youtu.be/P2QVCKrQzEI?...
The Rationals - I Need You (The Kinks cover 1965) (1966)
YouTube video by alpha bill
youtu.be
October 18, 2026 at 5:30 AM
1967 garage rock cover (The Kinks 1965) from Ann Arbor, MI. Michigan, Minnesota, Wisconsin; Illinois; Kansas & Texas all had pretty vibrant local garage rock scenes in the mid 1960s and small local record labels in the area to document the music.
#MusicSky youtu.be/P2QVCKrQzEI?...
#MusicSky youtu.be/P2QVCKrQzEI?...