ma𝕏pool

https://mathstodon.xyz/@maxpool

Question: How many people like me does it take to screw in a light bulb?
Answer: 0.9967±0.004 (after six iterations).

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nprofile1qqsqlwzgn5da55wsl8pjmsqgeey83v2q6c2xzt9ms0tzcv3ys48998cprpmhxue69uhhyetvv9ujumt0d4hhxarj9ecxjmntjy44y3

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Last Notes

2026-03-30 16:16:46 UTC

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This is just the beginning.
Current systems are the FORTRAN and Pascal of proof systems; they are for building pyramids--imposing, breathtaking, static structures built by armies pushing heavy blocks into place.
What we need is for someone to invent the Lisp of proof systems. Something that helps individuals to think new thoughts.

2026-03-29 17:53:06 UTC

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There is good reason to be conditionally optimistic right now.
If the fraction of planets capable of supporting life that actually develop it at some point (f1 in the Drake Equation) is on the order of 0.01 or higher, then it is only a matter of time. Astronomers have already found almost 50 candidates that are both rocky and in the habitable zone (25 if we are being conservative)
With sample size of one we have no idea what f1 is. If nothing is found as our catalogues grow and observations begin to reach observational limits, there will be good reason to become pessimistic again.

2026-03-26 15:08:27 UTC

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With MS you are fighting whack-a-mole with these "Dark Patterns" and "Deceptive Designs". It's never one-and-done.
"New Feature" loophole: After you have disabled something, MS introduces new feature than enables them again. Alternatively whenever they offer quick "Finish Settings" they set options again if you press Accept instead of going trough them one by one. Also update settings for something not-related.
https://media.mathstodon.xyz/media_attachments/files/116/296/061/051/306/322/original/9aec863b85c20873.png

2026-03-22 20:35:15 UTC

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I don't see any immediate reason to believe that people in Vietnam or Cambodia do not feel free when the question is "Are you satisfied or dissatisfied with your freedom to choose what you do with your life?"
Both countries are experiencing rapid economic growth (6-7% annually), urbanization, and cultural
transformation. This suggests there may be opportunities available and freedom to choose what to do.
Freedom to choose when people have high survival values and come from poverty is probably not as much about political freedoms or freedom of speech as it is elsewhere.

2026-03-22 18:47:01 UTC

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Correlates:
- real GDP per capita
- social support in times of trouble (often the strongest predictor of resilience and "floor" happiness)
- healthy life expectancy
- freedom to make life choices
- generosity
- perceptions of corruption
If asked about happiness from the previous day, Latin American countries would report being quite content or happy. That's probably related to strong community.
If people perceive life is OK, there is enough income, health, security, agency, and no feelings of severe injustice, they seem to default into happiness.

2026-03-18 08:57:19 UTC

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According to Wikipedia there is at least one 30 kW American Fission reactor in the Earth orbit: SNAP-10A
Several American satellites with RTG's (Radioisotope Thermoelectric Generators) are still in the Earth orbit. Mainly from the Transit series. Including SNAP-9A types using Pu238 as power source. https://en.wikipedia.org/wiki/List_of_nuclear_power_systems_in_space
"In April 1964 a SNAP-9A failed to achieve orbit and disintegrated, dispersing roughly 1 kilogram (2.2 lb) of plutonium-238 over all continents. Most plutonium fell in the southern hemisphere. " https://en.wikipedia.org/wiki/Systems_for_Nuclear_Auxiliary_Power
SNAP-10A:
https://en.wikipedia.org/wiki/SNAP-10A

2026-03-16 12:07:05 UTC

Why Are Viral Capsids Icosahedral?
Viral capsid structure is a geometric packing problem under genetic constraints.
https://www.asimov.press/p/viral-capsids
Virus symmetry and T number
Caspar-Klug Theory
https://viralzone.expasy.org/8577
Structural puzzles in virology solved with an overarching icosahedral design principle
https://www.nature.com/articles/s41467-019-12367-3
Capsid
https://en.wikipedia.org/wiki/Capsid
#biology #genetics #geometry #math
https://media.mathstodon.xyz/media_attachments/files/116/238/756/336/166/608/original/9a35270051ee1037.mp4

2026-03-13 09:23:14 UTC

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Currently for LLMs: If the model fits into memory and the context length is less than 32k, it's more cost-effective to run in your own PC.
https://mathstodon.xyz/@maxpool/116221057217529914
#note1wc0…ghev

2026-03-13 09:03:16 UTC

Consumer GPUs can reliably replace cloud inference for most SME workloads, except latency-critical long-context RAG, where high-end GPUs remain essential.
Self-hosted inference achieves cost parity with commercial APIs within 1–4 months at moderate usage (30M tokens/day), with subsequent operation at 40–200× lower cost than budget-tier cloud models.
Private LLM Inference on Consumer Blackwell GPUs: A Practical Guide for Cost-Effective Local Deployment in SMEs
https://arxiv.org/abs/2601.09527
"a systematic evaluation of NVIDIA's Blackwell consumer GPUs (RTX 5060 Ti, 5070 Ti, 5090) for production LLM inference, benchmarking four open-weight models"
"Consider dual-GPU configurations for consistent 32k+ workloads"
"Long-context benchmarks beyond 64k remain incomplete due to memory constraints."
#LLM #Nvidia #RTX #GPU #pc #cloud #datacenter
https://media.mathstodon.xyz/media_attachments/files/116/221/055/750/804/021/original/086f0a65c45bd3e7.png

2026-03-10 09:00:50 UTC

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(If you have ever felt that there is something weird about IHL and laws of war, continue reading)
Laws of war are dual use. IHL and the like do not exist just to reduce suffering, but to standardize and legitimize it in the public conscience so that war remains a tool of statecraft.
The 19th-century peace movements in the West were no joke. During the Hague Conventions, generals and legal minds determined what level of horror was militarily necessary and what level was economically or politically unsustainable. The conventions were the initiative of Tsar Nicholas II.. he and his ministers wanted to place limits on the lethal arms race because Russia was unable to compete.
The principle of superfluous injury, used to ban certain weapons, keeps a war something young men can volunteer into. In 1995, this principle was used to ban blinding laser weapons. A relatively easy method to permanently blind thousands of soldiers on the battlefield threatened the viability of war as a tool.
"You cannot qualify war in harsher terms than I will. War is cruelty, and you cannot refine it; and those who brought war into our country deserve all the curses and maledictions a people can pour out."
– Letter from William Tecumseh Sherman to James M. Calhoun, et al. (1864)

2026-03-03 22:06:32 UTC

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I agree. You must learn to use them productively. These systems are full of harms and misuse, but benefits and good uses.
I think the societal impact will get very bad before it get good. The quick buck comes from causing or ignoring harms.
https://infosec.exchange/@k3ym0/116161635202253362
#note1a29…gfzc

2026-03-03 17:22:58 UTC

Claude’s Cycles
Don Knuth, Stanford Computer Science Department
(28 February 2026; revised 02 March 2026)
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
#computerScience #algorithms #AI
https://media.mathstodon.xyz/media_attachments/files/116/166/395/012/101/739/original/f583abe2c265fa15.png

2026-03-02 23:52:44 UTC

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How was their economic organization because they were able to build so big things. I know the Aztec empire had city states and 'kings'. Palace economy? Government takes most and then redistributes.

2026-02-27 14:41:32 UTC

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We Will Not Be Divided
https://notdivided.org/
Google and OpenAI employees have released an open letter supporting Anthropic. #AI

2026-02-23 00:16:08 UTC

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Cognition and association-making don't require language.
Hard objects have give sharp transient acoustic signatures like kiki sound. Soft objects have slower rise times like bouba sound.
Crystal-like image on the left associates with hard, leaf-like image on the right associates with soft.

2026-02-22 23:50:35 UTC

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You are probably already familiar with applied category theorist Joseph A. Goguen, UCSD? He wrote "What is a concept?" (2005) https://cseweb.ucsd.edu/~goguen/pps/iccs05.pdf where he sketched a way to bring together cognitive, social, pragmatic and mathematical view of concepts and integrate them in same system.

2026-02-22 18:26:58 UTC

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There are other similar phenomena:
Vowel pitch: High pitch/small size low pitch/large size. (large objects vibrate with lower frequency)
Taste: Roundness equals sweet or creamy; angularity equals sour, bitter, or salty.
Grapheme-color synesthesia
There may be deep neurological reasons for conceptual metaphors, and these are just the lowest level. There are cultural mappings or individual level mappings developed later in life, such as spatial metaphors where the future is in front and the past is behind.

2026-02-13 17:54:42 UTC

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As I said, I don' t think this is necessarily bad thing.
Wikipedia shut down the experiment with short summaries angrily after a day, but users can get them through Google search snippets. They don't have to use Wikipedia proper.

2026-02-13 16:52:24 UTC

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I was talking primarily about readers, and I think the main point of the article was that it will become "irrelevant to younger generations of readers."

2026-02-13 10:53:27 UTC

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Jemielniak is a long-time Wikipedia activist and has served three terms on the Wikimedia Foundation Board of Trustees. He is also a professor who studies this specific area, so I give him the benefit of the doubt.
The main point of the article, as I see it, is that Wikipedia has a structure geared toward older generations. Young people don't read long articles, and older generations tend to calcify the organization.
I agree with all of the above. This also explains why there are fewer young volunteers. You don't become a contributor if you don't read the articles, especially if the style feels outdated or inconvenient.
On the other hand, I don't see anything wrong with projects that gradually decline in popularity while sticking to what the organization knows how to do. Wikipedia is losing readers and is becoming a more 'academic' and elite institution for new generations, but it still provides a valuable service.
---
A collaborative society should not mean that collaboration must happen within a single institution.
Wikipedia’s content is not bound to the organization itself; Gen Z and Gen Alpha can create their own organizations and short-form or conversational interfaces using Wikipedia as a source.
#wikipedia

2026-02-03 18:00:00 UTC

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Bush era prompted Naomi Wolf to write a book almost 20 years ago "The End of America: Letter of Warning to a Young Patriot" (2007) where she describes how societies close in 10 steps based on what happened after 9/11 in America.
1. Invoke a terrifying internal and external enemy.
2. Create secret prisons where torture takes place.
3. Develop a thug caste or paramilitary force not answerable to citizens.
4. Set up an internal surveillance system.
5. Infiltrate and harass citizens' groups.
6. Engage in arbitrary detention and release.
7. Target key individuals.
8. Control the press.
9. Cast criticism as espionage and dissent as treason.
10. Subvert the rule of law.
Those 10 things happened after 9/11 and were never fully rejected, legally or institutionally. Now, they are occurring on a different scale. It feels like an iterative development, with the severity increasing at each step.

2026-01-31 16:19:29 UTC

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Maybe it's not the freeze but "they wouldn't release the Epstein files until they are ready to attack Iran."
The day Trump attacked Venezuela was also the legal deadline for his DOJ to submit a written justification for all redactions in the Epstein case. Or was it the day after?

2026-01-20 18:06:38 UTC

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If I read your tone correctly, you think his remark is silly because it is so obliviously true.
I think it’s silly because he makes unfounded argument , one thing is not related to other. (he has made this argument several times btw.)
The massive success and wide adoption of life-changing technology does not, in itself, mean there is no bubble, nor does it guarantee that productivity will jump as Nadella suggests.
CEOs tend to think in terms of microeconomics, which behaves like an open system: 'a penny earned is a penny saved.' In this scale we are thinking in macroeconomics, which has closed-system dynamics and feedback loops: penny saved is not a penny earned.
In general its seems, that no matter how much you innovate technologically, the contribution is just 0.5-2.0 percent to economic growth due to all feedback loops in the system. On average just around 1%.
WP page on Productivity Paradox is a good intro:
https://en.wikipedia.org/wiki/Productivity_paradox
"You can see the computer age everywhere but in the productivity statistics." - Robert Solow

2026-01-18 14:49:36 UTC

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I don't know what you are in real life, I must only respond to what you wrote.
If you are what you say you are, maybe expresses it better and don't trivialize your own commitment.
(If you did read what I wrote, you understand that I'm not a pacifist.)

2026-01-18 14:33:38 UTC

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To me sounds like you are treating violence as entertainment, as an male power fantasy.
If you are going to discuss justified violence, do so with the sobriety and dignity that sacrifice and loss of life demands. To fantasize about executions without acknowledging the sacrifice is unserious and dehumanizing.
Huey P. Newton said: 'The first lesson a revolutionary must learn is that he is a doomed man.'"
If you are not a man violence you glorify, coaxing the young and (usually unstable young men) to go first while you have no intention of joining is low.

2026-01-17 17:24:07 UTC

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While violent resistance may be justifiable in some circumstances, internet posturing and the glorification of violence are both reprehensible and petty.

2026-01-16 16:09:49 UTC

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These points are taken directly from Mein Kampf. In the book, Hitler demonstrates a strong understanding of propaganda.
It is almost certain that Hitler was reading Gustave Le Bon's The Crowd: A Study of the Popular Mind (1895) while in prison writing Mein Kampf, as the parallels are undeniable. https://en.wikipedia.org/wiki/The_Crowd:_A_Study_of_the_Popular_Mind
Although Hitler does not mention Le Bon by name, he mentions Lord Northcliffe (who was in charge of British propaganda) and openly admired British propaganda during WWI. Northcliffe was enemy to emulate.
Later, Hitler likely learned from Edward Bernays through Goebbels, who admired American advertising techniques.

2026-01-14 22:12:13 UTC

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I thought only programmers had off-by-one errors.

2026-01-13 19:02:49 UTC

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As an experiment, I took screenshot from 12:56 and asked Gemini to do OCR that into text + latex. What a time to scribble notes.
---
Prob. that the spin is $\uparrow$ is
\[ |\langle \uparrow, v \rangle|^2 = |\langle (1,0), (v_1, v_2) \rangle|^2 \]
\[ = |v_1|^2 \]
Prob. that the spin is $\downarrow$ is
\[ |\langle \downarrow, v \rangle|^2 = |\langle (0,1), (v_1, v_2) \rangle|^2 \]
\[ = |v_2|^2 \]
https://media.mathstodon.xyz/media_attachments/files/115/889/303/800/529/702/original/bbb3b3c8b5073ce4.png

2026-01-06 09:39:59 UTC

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Parents also inherit gray hair from their children. At least, that's what my parents told me.

2026-01-03 15:56:00 UTC

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Just reserve a table at the Restaurant at the End of the Universe. Then, encode yourself and your entourage into an EM signal and send it on a trajectory that goes very near the event horizon of a black hole near the restaurant. The restaurant will capture your signal when the table is ready and put it through the meat printer.
(Alternatively, step into the cryochamber labeled 'Customers'. Note: DO NOT enter the cryochamber labeled 'Food' unless you are classified as sentient food.)

2026-01-02 19:07:07 UTC

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First story of time-dilation.
King Kakudmi once visited the Empyrean (called Brahmaloka by Hindus) to seek an audience with God (Brahma) and ask for advice regarding a suitable husband for his daughter.
After he presented the candidates, Brahma smiled and told him that all of them were already dead. Their sons, grandsons, and great-grandsons were all dust. He said, "In fact, while you waited here for these few moments, 27 chaturyugas (over 100 million years) have passed on Earth."
If I remember correctly, the same story is told slightly differently by different texts. In some versions, they had to wait for the audience because Brahma was listening to a musical piece; in others, the King listened to music while traveling. By the King's clock, the piece probably lasted only 20 minutes.
Either Brahma lives in a high gravity, or the king traveled very fast, or both.
https://en.wikipedia.org/wiki/Kakudmi
#scifi #mythology

2026-01-01 22:42:40 UTC

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Writing a random walk algorithm to find the solutions is more computer science than math. Only 30 minutes of computation on a standard laptop.
Math: Solution exists∎
Comp.sci: you can find the solution using these steps faster than brute force.

2026-01-01 16:08:26 UTC

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original unedited footage had different ending. 😀
https://media.mathstodon.xyz/media_attachments/files/115/820/702/042/932/037/original/f77357dae687a63e.mp4

2025-12-28 11:56:23 UTC

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"... they think that these journals have better reputation and they increase our chances of getting jobs and funding.. "
Are you implying that research funding and tenure tracks are no longer affected by the misuse of the Journal Impact Factor? Has something like DORA had a real cultural impact? If so, that's great news.
I was under the impression,perhaps based on outdated research, that the JIF is still widely used and has a significant effect on funding and careers.
https://blogs.lse.ac.uk/impactofsocialsciences/2019/04/26/the-impact-of-the-journal-impact-factor-in-the-review-tenure-and-promotion-process/

2025-12-27 01:06:46 UTC

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Some classics have permeated our culture so deeply that they are hard to enjoy as independent works of literature.
Don Quixote is called the best and most central work in world literature, and that's probably right. But when I try to read it, it feels derivative.
I know it's because Don Quixote is the first modern novel and everything else is derivative of it, but for me, it's the reverse because I have been exposed to the legacy of Don Quixote my whole life.
It's the same with Fritz Lang's movies. You watch them and they are just one cliché after another. Then you realize that Lang was the first to do them, and 80% of movies are just a rehash of the original.

2025-12-26 08:43:51 UTC

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Usually the reason is that some resource needed by the page comes from a slow site.
You can check it for yourself:
1. In Firefox/Chrome press F12 (Developer tools).
2. Go to "Network" tab
3. Reload the page.
4. Look for files that stay pending.
status and time columns should tell a story. When I try arXive abstracts it's fetching two files from https://cdn.jsdelivr.net/ that takes almost all time 500 ms. and 300 ms.

2025-12-16 17:34:45 UTC

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https://en.wikipedia.org/wiki/Force_majeure

2025-12-10 11:17:48 UTC

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If you know such a novel, how you recommend it without spoiling the twist?
I know novels with very similar twist you are asking for that leads you to revisit the novel in your mind after reading, but naming them will spoil them.

2025-12-06 11:39:19 UTC

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For all these questions the answer is Octopus (Gemini, new chat every time):
1. What is your favorite animal?
2. What animal you feel most kinship?
3. If you could choose a body to incorporate your intelligence, what animal body would you choose?
4. If humanity would be eradicated, what animal would most likely rule the Earth next?
5. What is the optimal physical form for intelligence? (from Embodied Cognition perspective)
The reasons it comes up are "alien intelligence", "radical adaptability", "distributed intelligence", "problem solving and dexterity"

2025-12-01 23:25:56 UTC

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My vote goes for for phlogiston.
The theory was that burning happens when material contains phlogiston.
- When things burn it releases phlogiston into the air and leaves ash.
- Plants absorb phlogiston from the air.
- Air has limited capacity to absorb phlogiston, this is why fire stops in closed space.
- CO2 was phlogisticated air.
- oxygen was dephlogisticated air.
- But when you burn metals, the as weighs more than original, thus phlogiston has negative mass.
and on and on, more complexity every iteration.
Solution: oxygen and oxidation, basically reverse of phlogiston theory.
https://en.wikipedia.org/wiki/Phlogiston_theory

2025-11-30 16:38:02 UTC

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Natural philosopher, formal philosopher, or formal scientist aka formalist might start a conversation better.
https://en.wikipedia.org/wiki/Formal_science

2025-11-29 14:01:00 UTC

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The way I see it, thermodynamic entropy is objective and irreversible, while information entropy can be subjective.
Reversible mixing does not significantly increase thermodynamic entropy. It's similar to folding clothes.
In reversible mixing you just lose the macroscopic indexing that is low entropy for you. It's like symmetric cryptography.

2025-11-28 14:03:24 UTC

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Biology has so much structure, but it's hard to abstract it into neat categories because most abstractions are leaky abstractions and everything can be repurposed at any time.
I see the definition of life being similar to the definition of money in economics. You can move smoothly from money to money-like, and previously non-money stuff can be repurposed as money in the right environment.

2025-11-28 10:24:41 UTC

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In addition to viral vector, bacteria are rampant parasexuals.
Bacterial evolution via horizontal gene happens daily. It can happen multiple different ways:
1. Viral transduction,
2. Transformation. picking free DNA fragments through the cell membrane.
3. Bacterial conjugation, via cell to cell contact using pilus https://en.wikipedia.org/wiki/Pilus
4. Some bacteria produce special gene transfer agents (GTAs) that are like virus phages, but they are bacteria's own way to transfer genetic material.
In animals, the gene transfer must happen in germline cells to affect species. It's rare but human genome has something like 8% old viral DNA.
It's my understanding that plants are between the two. Compared to animals it's easier to enter germline from stems that grow seeds, but it's harder to enter the cell.

2025-11-25 11:19:26 UTC

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The last time something this big happened was during the 4.2-kiloyear event. The Akkadian Empire was wiped out by a 300-year-long drought, the Indus Valley civilization collapsed, and the Old Kingdom in Egypt and the Liangzhu culture were all gone. https://en.wikipedia.org/wiki/4.2-kiloyear_event
Tehran will join long list of ancient ruins.

2025-11-19 16:33:23 UTC

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What is the difference between specifications for AI and humans? What is new?
Formal software specification has existed a long time. Leslie Lamport's TLA+ for example.
The problem is getting people to write formal verification. If this project is a success, I predict humans would just ask AI to write specifications for AI to write programs in.

2025-11-17 14:53:17 UTC

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Brain consumes about 20 Watts while running a model with ~500 trillion parameters.
That's efficient.

2025-11-17 14:20:04 UTC

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Thiel has has invested into smaller Nvidia competitors.
Michael Burry (who is famous for his correct 2008 bet against the US housing market) revealed that he has put options in both Nvidia and Palantir.

2025-11-12 10:39:31 UTC

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Sounds familiar, but I can't remember if I have read just this book. I have read few Macleod's books, they are readable space opera but unmemorable ... I can't remember what happens in them, just the vibe, style of writing.
I was interested in political/economical aspect and world building, but they are trope level.

2025-11-10 10:18:16 UTC

Duede E, Davey K. Apriori Knowledge in an Era of Computational Opacity: The Role of AI in Mathematical Discovery. Philosophy of Science. Published online 2025:1-11. doi:10.1017/psa.2025.10160 https://www.cambridge.org/core/journals/philosophy-of-science/article/apriori-knowledge-in-an-era-of-computational-opacity-the-role-of-ai-in-mathematical-discovery/0192BDB2814A219D9435A912786FE4CA
"Main Claim 2: We can (indirectly) gain apriori knowledge from the output of a computer program that is not mathematically transparent but which stores a (not necessarily human-checkable) proof of a mathematical claim. This is accomplished by employing a mathematically transparent proof-checker to evaluate the stored proof of the claim."
#philosophy #AI #mathematics

2025-10-28 14:04:24 UTC

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Wordpress has a guide how to add Creative Commons license to your page: https://wordpress.com/support/creative-commons/ If you add it into a proper template, it's done at once.

2025-10-28 13:50:35 UTC

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In that case, I recommend that you state your intention clearly with a Creative Commons (CC) license you prefer and attach it to your work. https://creativecommons.org/share-your-work/cclicenses/
Just because something is available does not mean that it can be used in good conscience when you don't give away any rights. A layman's ad hoc statement usually leaves something out and makes it less useful.
The CC0 Public Domain Dedication is the broadest and ensures the widest use.https://creativecommons.org/publicdomain/zero/1.0/legalcode.txt
If you want attribution, maybe CC BY 4.0

2025-10-28 11:23:12 UTC

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Suggestion: I think you should put your website and blog behind Cloudflare if they are not already, and use it to block AI crawlers or use their pay-per-crawl service https://blog.cloudflare.com/introducing-pay-per-crawl/
block: https://developers.cloudflare.com/bots/additional-configurations/block-ai-bots/
pay per crawl beta https://www.cloudflare.com/paypercrawl-signup/
Same for mathstodon.xyz btw. @npub197g…q2n4

2025-10-25 14:57:52 UTC

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She is making fun of ChatGPT's explanation. Then she goes on to explain positive geometry and Arkani-Hamed's work and gives it a positive review 1/10 on her 'physics bullshit meter.' It's not a zero because they haven't made any predictions yet.
(Minor point) She is not insulting Chinese people; she is using a typical German idiom that is equivalent to 'That's Greek to me' in English." https://en.wikipedia.org/wiki/Greek_to_me

2025-10-22 12:46:58 UTC

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As I was saying:
https://www.ebu.ch/news/2025/10/ai-s-systemic-distortion-of-news-is-consistent-across-languages-and-territories-international-study-by-public-service-broadcaste

2025-10-21 22:06:53 UTC

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Humans have very low in-group aggression, especially compared to chimps. Chimps exhibit a lot of violence within their group.
Humans can also extend the definition of in-group to include individuals they don't know personally, but I think this is culturally learned. Isolated human tribes are generally wary of outsiders.
Our out-group aggression can get very bad in both chimps and humans.

2025-10-19 18:08:13 UTC

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(more aislop if you are interested)
Same question verbatim for Gemini 2.5 Pro without any warmup.
"A vector A in ℂ³ gives a 3×3 matrix P = A* A. Here we are multiplying the column vector A by its conjugate transpose, which is a row vector A*, obtaining a 3×3 matrix P. If A has norm 1 then P² = P. But is this still true if we replace the complex numbers ℂ by the octonions 𝕆?"
It thinks a few minutes, knows the identity Claude did not know and shows a counterexample (I did not check, my Fano plane is in the hangar).
https://media.mathstodon.xyz/media_attachments/files/115/402/113/276/853/703/original/b276f1e932efc923.png
https://media.mathstodon.xyz/media_attachments/files/115/402/117/000/027/001/original/a976022fbc185fcf.png

2025-10-19 12:37:50 UTC

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Parameterintegralentdeckungslust just doesn't capture it.

2025-10-17 21:18:55 UTC

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Heh. Principia Mathematica is generally considered to be the most important scientific book ever published. But then "... This theorem remained largely unknown and undeveloped for over three centuries."
When Mark Twain said "A classic is something that everyone wants to have read, but nobody wants to read" he might have been into something.

2025-10-17 15:46:23 UTC

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For those who wonder, that's the third edition of Principia.
First editions can cost anything from several hundreds of thousands of dollars to $3.7 million. There are almost 400 known surviving copies of the Principia first edition.
The Internet makes us all Extremely rich: Philosophiae Naturalis Principia Mathematica by Isaac Newton https://www.gutenberg.org/ebooks/28233

2025-10-15 11:37:05 UTC

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What "a view" actually means is typically not much.
Something counts as a view on YouTube when it streams for at least 30 seconds (I've been told). Video analytics show things like average view duration, average percentage viewed, and watch time (hours).

2025-10-14 16:41:42 UTC

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I wonder if galaxies have Goldilocks zones for life, just like solar systems, where star density is low enough for supernovas not to sterilize planets every billion years.

2025-10-12 14:58:02 UTC

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I'm little baffled by the idea that our experience of art can betray us and that we should be on guard. I suppose all people experience art differently.
We all can all enjoy a sunset, sound of rain, or a beautiful rock not touched by human creativity, right? It's not called art, but it's equivalent to looking Jackson Pollock painting.
Would you feel better if there were someone equal to a DJ or turntablist who rotates knobs and alters the music AI generates?
Treq Lila from album by @npub1nf4…nqe4 https://math.ucr.edu/home/baez/music/treq_lila/6_treq_lila.mp3 It may or may not be relevant to the discussion 😲

2025-10-11 22:56:00 UTC

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Did BoE really warn about impeding AI disaster?
The article writer for Futurism did not read the BoE report; they used Reuters as their source. Reuters never links to the report it used in its reporting. I had to find it myself to get more than juicy quotes. https://www.bankofengland.co.uk/financial-policy-committee-record/2025/october-2025
This type of journalism is called churnalism–low value processing and rewriting press releases, wire service reports, and articles from other outlets to create "new" articles with little to no original reporting or fact-checking. Hopefully AI can replace this part of journalism soon.
Anyway. BoE report is better than any reporting about it. Maybe slightly more technical language.
#journalism

2025-10-11 20:09:58 UTC

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https://michael.orlitzky.com/documents/scans/vinberg_-_the_theory_of_convex_homogeneous_cones.pdf

2025-10-10 12:50:07 UTC

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Derek Lowe also wrote a piece about MOF.
The 2025 Nobel Prize in Chemistry: Metal-Organic Frameworks https://www.science.org/content/blog-post/2025-nobel-prize-chemistry-metal-organic-frameworks
These are fascinating.

2025-10-09 15:05:11 UTC

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Personally, I think inside the US Berkshire Hathaway (BRK.B) is the best option (P/E= 17 atm). When prices get too high, Berkshire just patiently waits and sits on a growing cash pile.
Berkshire is currently sitting on $344 billion USD in cash and cash equivalents. Third of their market cap is cash at the moment. They remain completely immune to Sam Altman's charm.
When you buy BRK.B today 30% of your investment is in bonds. After market crash, stocks naturally undershoot their long-run equilibrium values and they start seeing opportunities for using that money.
https://media.mathstodon.xyz/media_attachments/files/115/344/671/472/513/842/original/bf4f55055e69b990.png

2025-10-09 11:53:54 UTC

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Fast growth itself is not a bubble.
A "bubble" would mean an over-investment where the cash flow generated from data centers isn't sufficient to cover the capital invested in them and make profit.
I've repeatedly done napkin math as best I can, and I still can't see how this isn't a bubble.
At the same time, I remain optimistic about the total long-term impact of AI. While the current era of chatbots may be a temporary fad, the positive impact will become evident in robotics and other fields years from now.
---
I use Discounted Cash Flow (DCF) formula:
\[ DCF = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} + \frac{TV}{(1+r)^n} \]
where:
𝐶𝐹ₜ : cash flow for period (years)
r : discount rate (10% is typical)
n : number of periods (years).
TV: Terminal value past forecast.
Actual compute hardware might constitute 50% of the total data center investment and typically lasts only 3-5 years. The remaining data center infrastructure lasts longer.
For NVIDIA customers, covering the cost of just one year's investment in NVIDIA hardware ($120 billion in 2024) requires generating $30-50 billion in annual net cash profit. That's just one year of NVIDIA chips, they plan to buy more every year.
Stack subsequent years on top of each other and AI data centers must generate at least as much extra profits as Magnicificant-7 make now to be profitable. Not in the distant future but in next few years.
ps. The only way to power these systems in next few years is with natural gas turbines. The stock prices of the largest gas turbine manufacturers, such as GE Vernova Inc., Siemens Energy, and Mitsubishi Heavy Industries are soaring.
https://media.mathstodon.xyz/media_attachments/files/115/343/981/768/590/184/original/3251f5a3e4b77af8.png

2025-10-08 10:44:51 UTC

Philosophy of AI art.
@npub13hg…nysy
has interesting conditional take:
Let’s talk about AI art https://theoatmeal.com/comics/ai_art
"When I consume AI art, it also evokes a feeling, good, bad, neutral, whatever. Until I find out that it's AI art. Then I feel deflated, grossed out, and maybe little bit bored. ..."
If AI art is good enough, only the knowledge of how sausage is made can separate genuine enjoyment from disappointment.
Does this mean that only unsophisticated and naive people will feel the joy of enjoying art directly without the baggage of knowledge that spoils it?
Demand for organically produced art is real. Authenticity, being real, and artisanal qualities holds value in popular music, art, food, beverages, and general consumption. Marketing pushes it at every opportunity.
Previously, similar attitudes existed towards recorded music. Today, we allow ourselves to enjoy recorded music, though we still value live performances more. Picture: The robot playing nurse to the audience of the future (September 15, 1930 Capital Times).
#philosophy #AI #art
https://media.mathstodon.xyz/media_attachments/files/115/337/851/923/157/972/original/10abe7c8ddc007d1.webp

2025-10-05 13:52:23 UTC

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If you can find a lower risk-benefit analysis for coal production than for nuclear, I would like to see it.
We in the Finnish Green Party started changing our position on nuclear when we stopped using slogans and started quantifying and comparing risks.
No matter how you try to quantify the risk, it seems that the damage from coal is much larger than from nuclear. A Fukushima-level disaster every year would be less than equal amount of electricity from global coal production.
Coal is something 24 deaths per TWh in Europe.
Nuclear power is estimated to cause death per 14 years/TWh or so.
Coal ash is radioactive, contains arsenic, mercury and lead and often leaches into groundwater and streams. Then there is CO2, sulfur dioxide, nitrogen oxides.
From that perspective Germans should not have stopped working reactors.
Solutions for nuclear waste
Permanent storage
https://en.wikipedia.org/wiki/Onkalo_spent_nuclear_fuel_repository
Nuclear reprosessing
https://en.wikipedia.org/wiki/Nuclear_reprocessing

2025-10-05 13:28:02 UTC

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Germany got rid of nuclear too early.
Did not build energy storage to get rid of coal.
We must think in aggregate demand and production.
German energy consumption jumps “surprisingly” due to weak renewables output in early 2025
https://www.cleanenergywire.org/news/german-energy-consumption-jumps-surprisingly-due-weak-renewables-output-early-2025

2025-09-28 09:54:18 UTC

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Would there be "an imaginary surface such that you never cross it?" I think it still counts as event horizon.
What would photons flying directly towards singularity do? My intuition says that it would get closer and closer to the Schwarzschild radius, but never touch it.
Photons coming with an angle would be turned away. If a black hole is like a negative lens, a negative-mass black hole would be like a positive lens?
Is this correct?

2025-09-27 20:22:16 UTC

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He seems to account all data center energy use to compute (just cooling can be 40% of energy use) otherwise our math seems to be similar.
And somehow there must be money left to invest into crypto 😀
McKinsey estimates between $3.9 to $7 trillion between 2025-2030.
The cost of compute: A $7 trillion race to scale data centers https://www.mckinsey.com/industries/technology-media-and-telecommunications/our-insights/the-cost-of-compute-a-7-trillion-dollar-race-to-scale-data-centers
https://media.mathstodon.xyz/media_attachments/files/115/278/016/059/975/504/original/f710bee6b9eb6a0e.png
https://media.mathstodon.xyz/media_attachments/files/115/278/038/820/120/755/original/659b6b6b7f580973.png

2025-09-27 12:11:23 UTC

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The NVIDIA-OpenAI deal smells like the end phase of Dot-Com bubble. When investments dry out, and profits are not materializing, companies start to buy revenue.
But how much NVIDIA buys revenue? Below is my estimate, but maybe someone knows better.
NVIDIA promises to invest ~$10k/kW, when roughly 50% of a data center energy goes to actual compute. Lets assume Nvidia invests $20k/kW in their own hardware.
Using NVIDIA DGX B200 as reference:
Cost: ~$500,000
Power: ~14 kW
Total power use: ~28 kW
price/power: $17,000/kW.
Maybe I'm off a lot but with quick and dirty math any many assumptions it looks like they are buying their own hardware.

2025-09-25 18:35:36 UTC

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There is also Salvador Dali. Crucifixion (Corpus Hypercubus)
https://en.wikipedia.org/wiki/Crucifixion_(Corpus_Hypercubus)
https://media.mathstodon.xyz/media_attachments/files/115/266/354/356/848/707/original/d5e32b6a75113ae8.jpg

2025-09-23 08:47:03 UTC

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I believe those are called "κ-dense linear orders".

2025-09-22 11:47:09 UTC

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When using word aligned memory addressing you get always get additional 3 bits in 64-bit systems.
Different CPU's have supported tagging for ages but instruction level pointer tagging is not necessarily better or faster than masking by hand.
For numeric code NaN-tagging/NaN-boxing can be a performance boost. There is 52 bits available in 64-bit float 2^52-2 NaN's total. Some you want to use for actual NaN's, of course.

2025-09-21 11:50:36 UTC

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You are attempting to escape Numberland.
"Prisoners stand accused with a hypothesis with intent to prove, and contributing to the delinquency of a fraction."
Sunday cartoon where Georg Cantor escapes Numberland.
#cartoon #futurama #mathematics
https://media.mathstodon.xyz/media_attachments/files/115/242/116/918/064/597/original/5b7a7d5dea889514.mp4

2025-09-21 11:33:07 UTC

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Now I get, it.
Yes, cardinality of real numbers (or truly analog computer) is enough for hypercomputation.

2025-09-21 10:59:09 UTC

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The infinite size of the universe alone does not change what is computable.
Church–Turing thesis: A problem is uncomputable (non-computable) if a Turing machine can't compute it. Since a Turing machine already has an infinite tape, infinite space does not solve more problems than a Turing machine can.
To do what you want (hypercomputation), you need to add the ability to perform infinite steps in a finite amount of time, known as a "supertask" or "Zeno machine." This model can perform a countably infinite number of steps in finite time.
***
Computer scientists have thought about the relationship between computation and physics a bit (pun intended).
It's not the size of the universe, but rather general relativity that confines our computational universe.
If we assume that P≠NP is a physical law, stating that it's physically impossible to solve NP-complete problems in polynomial time, then physics seems to obey that law:
- Black holes limit how fast a computer can be.
- Relativity and speed of light limits how much computation can be distributed in space.
- Quantum mechanics must be linear to prevent hypercomputation, I think.
- And things like timeline curves must be impossible.
***
Scifi world building: A classical universe, Newtonian physics, infinitely divisible matter and space where you can build little robots that are faster and those robots build smaller robots that are faster, ....

2025-09-17 12:16:02 UTC

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A rotating object in space can periodically "turn over" because of the intermediate axis theorem, which says that rotation around the 2nd principal axis is not stable, while rotation around the 1st and 3rd is.
I think the condition is that the object must be rigid and have internal asymmetries that black holes can't have, since black holes have no "hair".
I assume this means that any change for black hole parameters must come from outside, except the evaporation. You can't have anything "sloshing inside the black hole" or can you?

2025-09-14 09:59:49 UTC

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Wikipedia says Thorne–Żytkow object is when neutron star collides with another star.

2025-09-12 10:30:00 UTC

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That is a miracle.
China in 2015 was like Britain in the 1950s. Choking in smog. Ten years later, it is leading the way and has increased primary energy consumption by 40%.
The lesson I draw from this is that big problems are usually political coordination problems, not technical problems.

2025-09-12 09:51:14 UTC

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(+) Chinese fossil fuel consumption has plateaued.
(−) Chinese coal exports have increased.
The global picture is all that matters in the end. Globally, coal, oil, natural gas demand is growing.
The real question is: When will global demand for energy grow slower than the increase in green energy? by how much?
Increasing renewable energy supply may increase global demand for fossil fuels for some time (Jevons paradox).
https://media.mathstodon.xyz/media_attachments/files/115/190/586/319/994/956/original/443b81c2e78fe4b4.png

2025-09-12 00:19:24 UTC

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Meanwhile...
Nature Index 2025 Research Leaders: United States losing ground as China’s lead expands rapidly
https://www.nature.com/nature-index/research-leaders/2025/nature-index-2025-research-leaders-united-states-losing-ground-as-chinas-lead-expands-rapidly.html
Although the latest data predate the current Trump administration, observers warn that funding cuts will accelerate the rate of China’s gain. ... China’s adjusted Share — which takes account of annual fluctuations in the volume of articles in the database year-on-year — jumped by 17.4% in the year to 2023. At the same time, the United States’ adjusted Share plummeted by 10.1%.
“China now employs more researchers than both America and the entire EU [European Union] combined,”

2025-09-10 13:06:18 UTC

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Not a math symbol. It's a symbol used in chess notation
2B96 EQUALS SIGN WITH INFINITY ABOVE
= with compensation for the material
page 308: https://www.unicode.org/charts/PDF/Unicode-17.0/U170-2B00.pdf

2025-09-08 11:59:42 UTC

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Wikipedia says water hammer is hydraulic shock when fluid in motion is forced to stop or change direction. Momentum converting into a pressure wave.
Inductive kickback seems to be analogical situation. When current (the fluid in motion) is switched off, the collapsing magnetic field causes short voltage spike (pressure wave).

2025-08-31 11:42:28 UTC

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People used to be more physical.
Traditions: Freshman-Sophomore Snowball Fight. Princeton class of 1895.
https://blogs.princeton.edu/wp-content/uploads/archive/aspire/2007/12/traditions_freshmans.html
https://media.mathstodon.xyz/media_attachments/files/115/123/181/181/286/188/original/3bc81a905bc71a31.webp

2025-08-30 14:41:25 UTC

Thinking the Way Animals Do: Unique insights from a person with a singular understanding.
By Temple Grandin, Ph.D.
Department of Animal Science
Colorado State University
(Updated January 2015)
https://www.grandin.com/references/thinking.animals.html
#cognition #philosophyofMind #autism

2025-08-30 13:28:57 UTC

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It's like sex without procreation.
People do useful things all day so that you have little time to do things that have intrinsic value for them.

2025-08-29 10:38:58 UTC

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I found that irritating as well, and I think most of his listeners feel the same way. That's our initial emotional response.
At the same time, my respect for his journalism just increases. He is not doing confirmation journalism for his in-group. Clearly, America is full of people who are not sufficiently worried, from left to right.
Trump is unpopular, but it's still over 40%, and his immigration policy is his most popular visible policy.
His net approval on immigration is just -3.8% negative. People like what they see, or don't know what they see, and many of them are not strong Trump supporters.
That German guy took over with much less popular support:
- July 1932: 37% of the vote.
- Nov 1932: 33% of the vote.
- 1933 elections were not free, thugs were sent to intimidate voters at the booth, but sill only 42% of the vote.

2025-08-24 13:49:15 UTC

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Those fed up with "business AI" should take a look into what really is going on.
The ARC challenge is now in its 3rd version and has its first 6 games publicly available for humans and AI developers to check out.
https://three.arcprize.org/
I like François Chollet's way of separating skills and intellect. Defining intelligence as broad or general-purpose skill-acquisition efficiency with some knowledge priors is a good working definition for developing AI. https://arxiv.org/abs/1911.01547

2025-08-23 09:31:50 UTC

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"In democracy you have to be a player" – Hunter S. Thompson, An Evening At Owl Farm
https://www.youtube.com/watch?v=NHeSC_Ws5Ic

2025-08-12 16:46:58 UTC

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A very common human trait.

2025-08-12 16:25:22 UTC

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I take back some of the "AI should know what they can't do, but they are not very good at it". I think Gemini is promising (we have all been there buddy 👍) :
"Google's Gemini AI tells a Redditor it's 'cautiously optimistic' about fixing a coding bug, fails repeatedly, calls itself an embarrassment to 'all possible and impossible universes' before repeating 'I am a disgrace' 86 times in succession
Two attempts later, Gemini declared itself "an absolute fool" for failing to identify a macro error. "This has been a marathon," the LLM said after four more tries, before declaring "this is the moment of truth." Immediately afterwards, it declared "I am defeated" and reentered the fray.
Gemini proceeded to make more than 20 additional debug attempts, its logging and comments growing steadily more despondent. At one point, it said it was at its "wit's end." Later, it named itself "a monument to hubris." Then, it was "a fool," "a broken man" with "no more ideas" who was "going to lose my mind."
https://www.pcgamer.com/software/platforms/googles-gemini-ai-tells-a-redditor-its-cautiously-optimistic-about-fixing-a-coding-bug-fails-repeatedly-calls-itself-an-embarrassment-to-all-possible-and-impossible-universes-before-repeating-i-am-a-disgrace-86-times-in-succession/

2025-08-12 08:45:20 UTC

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That's a good observation that makes sense.
Imagine if people had a reverse visual cortex, a reverse optic nerve, and a reverse retina attached to a projector in their forehead.
Smallest details would be smudge when we try to imagine things.

2025-08-12 08:30:06 UTC

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Impressive feat of machine learning, but a very unsatisfying product.
Remember, these are not LLMs drawing something; they are doing generative recall.
A popular trick to determine if you're in a dream is to try reading a book; if the letters are a jumbled mess, you're dreaming. LLM outputs share this and many other features with human dreams.
Imagine having a dream where someone asking you to visualize a map of the US and name all the states in that visualization. I bet you could not do that as well.
ps. I asked the same from Google's Gemini 2.5 pro. It did not try to generate a map, instead it gave a map licensed by Google. That's not impressive AI, but better product.
AI products should know what they can't do, but they are not very good at it. They think they can fly, just like we do when we are dreaming.
https://media.mathstodon.xyz/media_attachments/files/115/014/817/518/265/234/original/e2d7c4e1267b1001.jpeg

2025-08-05 16:35:06 UTC

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This is interesting, apparently there is a step in how students think limits. 0.999.. as process that continues infinitely long, vs fixed number.
Tall, David (2000). "Cognitive Development in Advanced Mathematics Using Technology" Mathematics Education Research Journal. 12 (3): 210–230.
https://web.archive.org/web/20090530043111/http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot2001b-merj-amt.pdf
"A full session was dedicated to discussing how an infinite decimal can be seen as the limit of the sequence of finite decimal approximations. Specific attention was given to explaining why the infinite decimal 0.9 (nought point nine repeating) is the limit of the sequence (1–1/10n), and is therefore 1. Despite this discussion, the meaning of 0.9 remained essentially unchanged two weeks later."
...
"We thus see that the underlying beliefs of students reveal a widespread variety of concept images of the nature of number and limit that are only partially solved by attempts at teaching. Other research confirms this viewpoint (e.g., Williams, 1992). One of the major underlying reasons for students’ unwillingness to accept a definition in axiomatic mathematics is that, up to this point, the student was used to having definitions that describe already existing concepts that are familiar to them. They are not, at this stage, willing to accept an axiom that does not correspond to something that they already know. The problem with using the
completeness axiom as a basis for the theory of convergence is that it does not agree with students’ previous experience. How can such an axiom be the basis of a theory, if it is clearly untrue?"

2025-08-05 10:53:50 UTC

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When people claim that 0.999... is not equal to 1, mathematicians get confused because they don't understand why students don't understand, even after a simple proof.
It's because you guys are proving features of decimal notation with algebra. It's bad pedagogy. It creates cognitive dissonance.
If different notation means a different number is the starting axiom (an implicit, unconscious framing), then proving that they are equal makes algebra seem inconsistent.
A conceptual separation between decimal notation and the number it refers to should be the first thing.
Teaching decimal notation separately, and not as part of elementary algebra, and making that distinction clear is, in my humble opinion, the only pedagogically correct way.
Does anyone disagree?