Garrett Baker

Karma: 6,485

I have signed no contracts or agreements whose existence I cannot mention.

They thought they found in numbers, more than in fire, earth, or water, many resemblances to things which are and become; thus such and such an attribute of numbers is justice, another is soul and mind, another is opportunity, and so on; and again they saw in numbers the attributes and ratios of the musical scales. Since, then, all other things seemed in their whole nature to be assimilated to numbers, while numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number.

Metaph. A. 5, 985 b 27–986 a 2.

Garrett Baker 2 Feb 2026 17:19 UTC

13 points

in reply to: lalaithion’s comment on: Thoughts the Unreasonable Effectiveness of Maths

Here is the claimed Gorard’s “alien logic system” in the linked tweet

I had Claude chew on this for a bit, and Claude determined that this proof system was the trivial one (ie ∀a,b:a=b) by writing a script in SPASS (an automatic theorem prover) to try to prove this statement.

Here is the SPASS proof

--------------------------SPASS-START-----------------------------
Input Problem:
1[0:Inp] || equal(skc2,skc3)** -> .
2[0:Inp] ||  -> equal(op(op(u,v),op(v,u)),v)**.
3[0:Inp] ||  -> equal(op(op(u,v),v),op(v,op(v,u)))**.
4[0:Inp] ||  -> equal(op(op(u,op(v,w)),w),op(v,op(u,op(w,u))))*.
 This is a unit equality problem.
 This is a problem that has, if any, a non-trivial domain model.
 The conjecture is ground.
 Axiom clauses: 3 Conjecture clauses: 1
 Inferences: IEqR=1 ISpR=1 ISpL=1 
 Reductions: RFRew=1 RBRew=1 RFMRR=1 RBMRR=1 RObv=1 RUnC=1 RTaut=1 RFSub=1 RBSub=1 
 Extras    : Input Saturation, No Selection, No Splitting, Full Reduction,  Ratio: 5, FuncWeight: 1, VarWeight: 1
 Precedence: op > skc3 > skc2 > skc1 > skc0
 Ordering  : KBO
Processed Problem:

Worked Off Clauses:

Usable Clauses:
1[0:Inp] || equal(skc3,skc2)** -> .
2[0:Inp] ||  -> equal(op(op(u,v),op(v,u)),v)**.
3[0:Inp] ||  -> equal(op(op(u,v),v),op(v,op(v,u)))**.
4[0:Inp] ||  -> equal(op(op(u,op(v,w)),w),op(v,op(u,op(w,u))))*.
	Given clause: 1[0:Inp] || equal(skc3,skc2)** -> .
	Given clause: 2[0:Inp] ||  -> equal(op(op(u,v),op(v,u)),v)**.
	Given clause: 3[0:Inp] ||  -> equal(op(op(u,v),v),op(v,op(v,u)))**.
	Given clause: 15[0:Rew:3.0,14.0,2.0,14.0] ||  -> equal(op(u,op(u,v)),op(v,op(v,u)))*.
	Given clause: 4[0:Inp] ||  -> equal(op(op(u,op(v,w)),w),op(v,op(u,op(w,u))))*.
	Given clause: 11[0:SpR:3.0,2.0] ||  -> equal(op(op(u,op(u,v)),op(u,op(v,u))),u)**.
	Given clause: 16[0:SpR:15.0,2.0] ||  -> equal(op(op(op(u,v),u),op(v,op(v,u))),u)**.
SPASS V 3.9 
SPASS beiseite: Proof found.
Problem: collapse.dfg 
SPASS derived 171 clauses, backtracked 0 clauses, performed 0 splits and kept 96 clauses.
SPASS allocated 85510 KBytes.
SPASS spent	0:00:00.08 on the problem.
		0:00:00.03 for the input.
		0:00:00.02 for the FLOTTER CNF translation.
		0:00:00.00 for inferences.
		0:00:00.00 for the backtracking.
		0:00:00.01 for the reduction.


Here is a proof with depth 3, length 23 :
1[0:Inp] || equal(skc3,skc2)** -> .
2[0:Inp] ||  -> equal(op(op(u,v),op(v,u)),v)**.
3[0:Inp] ||  -> equal(op(op(u,v),v),op(v,op(v,u)))**.
4[0:Inp] ||  -> equal(op(op(u,op(v,w)),w),op(v,op(u,op(w,u))))*.
14[0:SpR:2.0,3.0] ||  -> equal(op(op(u,v),op(op(u,v),op(v,u))),op(u,op(u,v)))**.
15[0:Rew:3.0,14.0,2.0,14.0] ||  -> equal(op(u,op(u,v)),op(v,op(v,u)))*.
16[0:SpR:15.0,2.0] ||  -> equal(op(op(op(u,v),u),op(v,op(v,u))),u)**.
17[0:SpR:15.0,2.0] ||  -> equal(op(op(u,op(u,v)),op(op(v,u),v)),op(v,u))**.
34[0:SpR:4.0,2.0] ||  -> equal(op(op(u,op(v,op(w,u))),op(w,op(v,op(u,v)))),op(v,op(w,u)))**.
49[0:SpR:4.0,2.0] ||  -> equal(op(op(u,op(op(op(v,u),u),v)),v),u)**.
63[0:Rew:3.0,49.0] ||  -> equal(op(op(u,op(op(u,op(u,v)),v)),v),u)**.
128[0:SpR:16.0,3.0] ||  -> equal(op(op(u,op(u,v)),op(op(u,op(u,v)),op(op(v,u),v))),op(v,op(u,op(u,v))))**.
145[0:SpR:3.0,16.0] ||  -> equal(op(op(op(u,op(u,v)),op(v,u)),op(u,op(u,op(v,u)))),op(v,u))**.
168[0:Rew:17.0,128.0] ||  -> equal(op(op(u,op(u,v)),op(v,u)),op(v,op(u,op(u,v))))**.
171[0:Rew:168.0,145.0] ||  -> equal(op(op(u,op(v,op(v,u))),op(v,op(v,op(u,v)))),op(u,v))**.
173[0:Rew:34.0,171.0] ||  -> equal(op(u,op(u,v)),op(v,u))**.
174[0:Rew:173.0,15.0] ||  -> equal(op(u,op(u,v)),op(u,v))**.
194[0:Rew:173.0,63.0] ||  -> equal(op(op(u,op(op(v,u),v)),v),u)**.
209[0:Rew:173.0,174.0] ||  -> equal(op(u,v),op(v,u))*.
228[0:Rew:173.0,194.0,209.0,194.0,173.0,194.0,173.0,194.0,209.0,194.0] ||  -> equal(op(u,v),u)**.
229[0:Rew:228.0,2.0] ||  -> equal(op(u,v),v)**.
234[0:Rew:228.0,229.0] ||  -> equal(u,v)*.
235[0:UnC:234.0,1.0] ||  -> .
Formulae used in the proof : conjecture0 axiom1 axiom0 axiom2

--------------------------SPASS-STOP------------------------------

Here is Claude’s proof summary

Proof sketch (from SPASS, depth 3, length 23):

Axioms 1 & 2 ⟹ a ⊕ (a ⊕ b) = b ⊕ (b ⊕ a) [step 15: “symmetrized absorption”]
Substitutions into Axiom 3 + rewrites ⟹ a ⊕ (a ⊕ b) = b ⊕ a [step 173: “double apply = flip”]
(1) + (2) ⟹ a ⊕ (a ⊕ b) = a ⊕ b [step 174: idempotent-like]
(2) + (3) ⟹ a ⊕ b = b ⊕ a [step 209: commutativity]
(4) + earlier lemmas ⟹ a ⊕ b = a [step 228: left absorption]
Rewrite Axiom 2 with (5) ⟹ a ⊕ b = b [step 229: right absorption]
(5) + (6) ⟹ a = b ∀ a,b ∎

Therefore I think its quite likely that many of the supposedly rich alien axiom systems Gorard found are actually just trivial almost-contradictory systems which are hard to prove the triviality of. It also explains why he couldn’t “make sense” of the system. There is nothing to make sense of.

Garrett Baker 30 Jan 2026 3:03 UTC
19 points
11
in reply to: Ben Pace’s comment on: Problems with “The Possessed Machines”
I think the content and arguments in the possessed machines are not very good, the prose is ok but it would read as too self important and AI slop on a less distinguished webpage. I think that many people were charmed by how respectable and nice the website looked and so were willing to give the writing and arguments much more leeway when sharing the page (if they read it at all).

Edit: I believe this because I notice it is popular, and I noticed this dynamic in myself, I felt I wanted the article to be deep and interesting, but also that if I thought about telling the arguments to a skeptical observer very few of them would stand up to scrutiny.

Garrett Baker 30 Jan 2026 1:39 UTC
5 points
1
on: Problems with “The Possessed Machines”
Yeah, the possessed machines is a very good example of how important good web design is.

Lighthaven Sequences Reading Group #67 (Tuesday 1/27)

Garrett Baker and Ben Pace

26 Jan 2026 19:15 UTC

9 points

1 comment1 min readLW link

Garrett Baker 26 Jan 2026 4:29 UTC
0 points
4
in reply to: koanchuk’s comment on: koanchuk’s Shortform
If you are to make claims like this, at least make arguments. This isn’t twitter.

Garrett Baker 24 Jan 2026 19:59 UTC
5 points
0
in reply to: Eli Tyre’s comment on: Habryka’s Shortform Feed
Caro is extremely comprehensive and will write small mini-books on the history of every significant institution or person LBJ ever touched. That means that The Master of the Senate begins in like 1810 and gives a complete history of the Senate up until LBJ is elected into the body.

Garrett Baker 24 Jan 2026 6:10 UTC
2 points
0
in reply to: habryka’s comment on: Habryka’s Shortform Feed
I would be interested in someone analyzing when the constitution would permit a private citizen to take up arms against a sitting government (if any such circumstance exists).

To my knowledge, the interpretation which comes closest is Insurrectionist theory which interprets the right to bear arms as including the right of citizens to use them to defend against an oppressive government. There are apparently more explicit statements of this right in the preambles to some first-state constitutions, as well as the declaration of independence.

It should not be surprising that nobody has yet won on such a case in court though, and practically speaking you don’t have this right ^[1] .

My understanding has been that even if you are arrested unlawfully by a police officer, you can’t use proportional force (as you would if you were assaulted by a non-police-officer), since the perspective of the government is that it is the judiciary’s right to determine whether an arrest is or isn’t lawful, not the citizen’s.
1. ↩︎
  Except implicitly the founders themselves, who of course supported the right to revolution. Or at least supported that right for themselves. But originalism has never been a popular (or coherent) constitutional philosophy.

Garrett Baker 24 Jan 2026 5:05 UTC
6 points
2
in reply to: AlphaAndOmega’s comment on: Habryka’s Shortform Feed
Yeah I meant “most” where the others we’re comparing are the 9 justices and one Marshal at most.

Garrett Baker 24 Jan 2026 5:04 UTC
10 points
4
in reply to: Eli Tyre’s comment on: Habryka’s Shortform Feed

But I would eagerly read a post describing how this change came about and what downstream factors it impacted.

I cannot recommend more strongly the first three chapters of Robert Caro’s Master of the Senate on this subject. It gives a full political history of the senate, and essentially its fall from grace, starting as the most powerful single component of the US government, hailed the world over for being the most competent and thoughtful political organization on the planet, to its ineptitude becoming the butt of jokes on TV and barely being considered during the signing of routine treaties.

Garrett Baker 23 Jan 2026 18:04 UTC
12 points
2
in reply to: habryka’s comment on: Habryka’s Shortform Feed
Yeah, I remember in high school civics I could not understand in what sense the tripartite system of government we have constituted a “balance of powers”, when the only branch of government with any meaningful amount of guns was the executive, ruled by a singular president ^[1] .

Until very recently it felt like a miracle anything worked at all, and my impression is that it worked so well in the past because congress had much much more day-to-day decision making power and was much more plugged into the information sources, then the “seniority system” was instantiated, congress became senile, and FDR got unprecedented control over the war-time economy, and took the opportunity to transfer many decision making roles and bodies from congress to the executive.

When congress is made up of the old and senile, and relies on the president to be their eyes, ears, hands, and brain, it just makes more and more sense to delegate broader and broader powers to the executive, who has the better qualified staff, more information, and a quicker reaction time.

The courts have never been all that powerful, except when they had the implicit backing of the president or congress. When they haven’t clearly had that, my impression is they have made sure not to command the executive to take any meaningful actions.
1. ↩︎
  My teacher’s response to these questions & my confusion over their responses was kick me out of the classroom into the hallway. I gained quite a positive reputation among students and teachers after that!

Garrett Baker 23 Jan 2026 18:00 UTC
5 points
2
in reply to: jmh’s comment on: Habryka’s Shortform Feed

Could you point to your source for the claim about the Marshall’s Service falling under the Judicial Branch of the government? My understanding is that his belongs to the DoJ so would fall under the Executive Branch.

I believe this is a minor mistake, see my other comment.

Garrett Baker 23 Jan 2026 17:56 UTC
54 points
4
in reply to: habryka’s comment on: Habryka’s Shortform Feed

These guns come in the form of the U.S. Marshalls who are under the direct control of the judicial branch.

You got the (admittedly extremely confusing) names wrong here. The US Marshalls are under the executive branch and report to the Attorney General, however the Marshal of the United States Supreme Court is a single person under the direct command of the supreme court and heads the Supreme Court of the United States Police Department, who are actually the people with most of the guns here.

This seems like its caused some confusion with some commenters here.
What links here?
- Garrett Baker's comment on Habryka’s Shortform Feed by habryka (23 Jan 2026 18:00 UTC; 5 points)

Garrett Baker 23 Jan 2026 17:47 UTC
4 points
0
in reply to: jmh’s comment on: Habryka’s Shortform Feed

what if the banking system refused to honor them given the S.C and Congress’s rulings?

This is one reason why the independence of the FED is important. The US has a very centralized banking system which is technically governed by the executive branch.

Garrett Baker 23 Jan 2026 17:42 UTC
7 points
2
in reply to: Oliver Sourbut’s comment on: Habryka’s Shortform Feed
I have heard this claim before, but have never been given a reason to believe it. Why do you believe the military is under the spell of “listen to the constitution” and not “listen to orders”? The latter seems a far more prevalent sentiment given the practical fact that often if you don’t listen to orders, you and your friends will often wind up dead.

Garrett Baker 20 Jan 2026 21:26 UTC
3 points
0
in reply to: 1a3orn’s comment on: ricraz’s Shortform

I think this is a really big part of why the free market of ideas has stopped working in the US over the last decade or two.

Say more on this? I don’t see the argument. It’s also not clear why this would only affect the US for instance.

Garrett Baker 20 Jan 2026 20:34 UTC
3 points
0
in reply to: kuilin’s comment on: Lighthaven Sequences Reading Group #66 (Tuesday 1/21)
oops, yeah. Thanks

Lighthaven Sequences Reading Group #66 (Tuesday 1/20)

Garrett Baker and Ben Pace

20 Jan 2026 18:58 UTC

8 points

2 comments1 min readLW link

Garrett Baker 20 Jan 2026 16:24 UTC
2 points
0
in reply to: StanislavKrym’s comment on: Five Theses on AI Art
It’s not clear to me this would increase the quality level of what gets spread. First, the few selectors likely have as bad taste as the hoi polloi, being selected for political acumin for what is, essentially, a political job, if they are selected for anything. Second, it is widely agreed that art flourishes on subversion and going “against the pack”, with many (especially of the old guard) hating new art forms when they arrive. Third, such selection will necessarily cater to the lowest common denominator. Compare TV shows of the ’90s to TV shows now.

Garrett Baker 19 Jan 2026 8:13 UTC
2 points
0
in reply to: Viliam’s comment on: Should you be posting on the open internet
Hm. So the two situations are:
1. Alice sends Bob an email containing text $T$ , and Bob tells Charlie “Alice said $T$ ″!” and sends a screenshot of the email. Charlie, convinced, sanctions Alice for saying $T$ .
2. Alice tells Bob a statement $T$ in a pub, and Bob tells Charlie “Alice said $T$ ″!”. However, Alice hears that Bob told Charlie this, and denies she ever said $T$ . Charlie believes Alice, or at least is left with enough uncertainty not to sanction Alice for saying $T$ .
I guess I don’t understand why Alice can’t deny having sent Bob $T$ in an email in situation 1. Bob could have made up the text just as much as he could have made up the statement in 2, especially now, in the age of LLMs. Maybe Alice also sent a signature cryptographically verifying they sent $T$ , however simply not sending that signature seems easier than abandoning email as a medium for this type of communication.

Edit: There are also other solutions here, like automatically deleting messages before webscrapers can touch them, or using the anonymity still by default provided by the internet.

Garrett Baker 19 Jan 2026 8:01 UTC
6 points
0
in reply to: StanislavKrym’s comment on: Five Theses on AI Art
You could apply the same thing to any new genera of art. The hoi polloi all have horrible taste, and therefore we should expect the new genera to mostly cater to that horrible taste and produce a ton of slop.

On the one hand, that’s true. New artistic media and generas often result in a greater amount of slop produced. But it misses the fact that new artistic media and generas also create artistic innovation, and while only a small minority of people have good taste, often (especially in the long term), the market accommodates that good taste just fine, and we get masterworks of that new media or genera.

Garrett Baker

Lighthaven Se­quences Read­ing Group #67 (Tues­day 1/​27)

Lighthaven Se­quences Read­ing Group #66 (Tues­day 1/​20)

Lighthaven Sequences Reading Group #67 (Tuesday 1/27)

Lighthaven Sequences Reading Group #66 (Tuesday 1/20)