https://x.com/getjonwithit/status/2035052237777486024 - Bull doze vs Nautilus machine in AI autoformalization
Saturday, March 21, 2026
Friday, March 20, 2026
How expensive did the printing press make suppression of ideas
"The printing press did not merely spread information; it made the suppression of ideas ruinously expensive. " - https://x.com/ani_pai/status/2031042753015013462
Analysis by chatgpt---
Short answer: even a moderately successful early printed work could already be beyond practical “recall” after a single print run. The numbers were small by modern standards—but large enough, and dispersed enough, to make clawing them back extremely costly.
Here’s what that looked like in real terms:
Typical print runs (15th–16th century)
Early books (incunabula, before 1500): ~100–300 copies per edition
By the early 1500s: ~300–1,000 copies was common
Cheap pamphlets (like religious tracts): sometimes 1,000–3,000+ copies
That might sound tiny—but the key is distribution and multiplication over time.
Example: Martin Luther’s writings
During the Protestant Reformation:
Luther’s early pamphlets (1517–1520) are estimated to have sold 300,000+ copies within a few years
Individual pamphlets often had 1,000–2,000 copies per print run
Successful texts were reprinted across dozens of cities
So even if you stopped one printer, 10–20 other presses might already be producing the same text.
Why “clawing back” was so expensive
Imagine trying to suppress a single controversial book with a 1,000-copy print run:
1. Geographic spread
Copies weren’t sitting in one warehouse:
Sold across multiple cities and regions
Carried by merchants, students, clergy
To retrieve them, authorities would need:
Messengers, inspectors, and local enforcement in each place
Coordination across political boundaries (often impossible)
2. Private ownership
Once sold:
Books belonged to individuals
You’d need house-to-house searches or incentives for surrender
Both options are expensive and socially disruptive
3. Reprinting already underway
Even if you recovered, say, 70–80% of copies:
Printers could reset type and produce new editions quickly
Other printers (in different jurisdictions) might already be copying it
4. Enforcement costs scale badly
Cost grows faster than the number of copies:
100 copies → manageable
1,000 copies → regional effort
10,000+ copies → essentially uncontrollable
A useful way to think about it
In manuscript culture (pre-printing):
50 copies might exist
Confiscating them = feasible
In print culture:
1,000 copies exist → spread across 10–20 cities
Plus reprints → total circulation keeps growing
So the “cost” isn’t just per copy—it’s:
Cost of policing an expanding network of readers, printers, and borders
Bottom line
Even a single successful print run (a few hundred to a thousand copies) could push an idea past the point where recovery was realistic. Once a text hit multiple print runs across cities—as with Reformation pamphlets—the cost of suppression wasn’t just high; it became effectively infinite relative to the resources of any single authority.
If you want, I can walk through a rough “budget model” (what it might cost a 16th-century state in manpower and money to try to recover 1,000 copies).
Let’s build a rough, historically grounded “suppression budget” for a 16th-century authority trying to claw back a single controversial book after one successful print run.
Scenario setup
Print run: 1,000 copies
Spread across: 10 cities
Time since release: a few months
Goal: recover or destroy as many copies as possible
We’ll assume this is happening somewhere in the Protestant Reformation era, when censorship was actively attempted.
Step 1: What does a book cost (for context)?
A book might cost ~0.5 to 1 florin
A skilled worker’s daily wage: ~0.5–1 florin
So each book represents roughly a day’s wages
π Buying back 1,000 copies at market price:
~500–1,000 florins
That’s already significant—but it’s actually the cheapest part.
Step 2: Administrative + enforcement costs
To retrieve books, authorities would need:
Personnel per city (×10 cities)
1 commissioner or magistrate
2–5 assistants or clerks
5–10 guards or enforcers
Let’s say 10 personnel per city → 100 people total
Duration
Investigation + enforcement: ~30 days
Wage cost
Average: ~0.5 florin/day
π Labor cost:
100 people × 30 days × 0.5 florin
= 1,500 florins
Step 3: Travel, logistics, and coordination
Messengers between cities
Transport (horses, carts)
Lodging + food
π Estimated:
300–600 florins
Step 4: Compliance costs (the hard part)
You can’t just seize everything easily. So authorities often:
Offer buybacks above market price
Pay informants
Fine or pressure sellers (which has enforcement costs)
Let’s assume:
Only 60% compliance voluntarily
Need incentives + enforcement
π Extra costs:
Buyback premiums + informants: 500–1,000 florins
Step 5: Losses due to failure
Even after all this:
20–40% of copies likely remain hidden
Some are already copied or reprinted elsewhere
So:
You might spend thousands of florins and still fail
Total estimated cost
| Category | Cost (florins) |
|---|---|
| Buyback (base) | 500–1,000 |
| Labor | ~1,500 |
| Logistics | 300–600 |
| Incentives / enforcement | 500–1,000 |
| Total | ~2,800 to 4,100 florins |
What does that mean in context?
A craftsman’s annual income: ~150–300 florins
So this operation costs the equivalent of:
π 10–25 years of skilled labor income
And that’s for just 1,000 copies of one book.
Why this becomes “ruinous”
Now scale it:
Multiple print runs
Multiple texts
Multiple cities and jurisdictions
This is exactly what happened with figures like Martin Luther—where suppression required ongoing, multi-year campaigns.
At that point, authorities face a brutal equation:
The marginal cost of suppressing each additional copy or edition rises, while the probability of success falls.
The deeper insight
The printing press didn’t make ideas unstoppable—it made them:
Cheaper to produce than to suppress
Faster to spread than to contain
Distributed beyond any single authority’s reach
So even though 1,000 copies sounds small, economically it was enough to flip the balance of power.
If you want, we can compare this to modern digital information (where the “cost to copy” is basically zero) and see how the same dynamic has gone even further.
Thursday, March 19, 2026
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Thursday, March 12, 2026
Wednesday, March 11, 2026
What did Paul Erdos quip about aliens and R(6,6)
The statement “AlphaEvolve has helped establish new lower bounds for five classical Ramsey numbers” is significant because it represents progress in one of the hardest areas of combinatorics and theoretical mathematics. To understand why it matters, we need to unpack a few pieces.
1. What Ramsey numbers are
Ramsey numbers come from Ramsey Theory, which studies when order must appear inside randomness.
A Ramsey number (R(m,n)) asks:
What is the smallest number of people needed at a party so that either at least (m) people all know each other or at least (n) people are all strangers?
Example:
Ramsey number R(3,3) = 6
Meaning:
In any group of 6 people, there must be either:
3 mutual friends, or
3 mutual strangers.
For larger numbers (like (R(5,5)), (R(6,6))), the values become extremely hard to determine.
2. Why Ramsey numbers are notoriously difficult
Most Ramsey numbers are unknown.
For example:
Ramsey number R(5,5) is only known to be between 43 and 48.
For larger ones, the uncertainty ranges can be hundreds or thousands wide.
Mathematicians usually try to prove:
Lower bound: the number is at least some value
Upper bound: the number is at most some value
Closing the gap between these bounds is a major research challenge.
3. What a “new lower bound” means
If researchers show a larger lower bound, it means they discovered a specific structure that avoids the forced pattern longer than previously known.
Example idea (simplified):
Previously:
Largest known graph avoiding the pattern: N = 42
New result:
Someone constructs one with N = 44
Now we know:
[
R(m,n) > 44
]
That’s a new lower bound.
Even improving by 1 can be a major breakthrough.
4. What AlphaEvolve did
AlphaEvolve is an AI system developed by Google DeepMind that searches for mathematical structures.
Instead of proving theorems directly, it:
Generates candidate graphs
Tests whether they avoid certain forbidden patterns
Evolves better structures using search and optimization
Using this process, it discovered larger graphs without certain cliques or independent sets, improving known bounds.
So when you read:
“AlphaEvolve established new lower bounds for five classical Ramsey numbers”
it means:
The AI found better constructions than humans previously knew.
Those constructions push the known limits of these Ramsey numbers.
5. Why this is a big deal
There are several reasons mathematicians care:
1. These problems can remain unsolved for decades
Some Ramsey bounds haven't improved in 20–30 years.
2. The search space is astronomically large
For graphs with 40–50 vertices there are more possibilities than atoms in the universe.
AI can explore this space far more aggressively than humans.
3. It shows AI can assist pure mathematics
Similar to:
AlphaGo (games)
AlphaFold (biology)
AlphaEvolve suggests AI may become a tool for discovering new mathematical objects.
✅ In simple terms:
The significance is that an AI system discovered better examples of large pattern-avoiding graphs, which pushed forward the known limits of several Ramsey numbers—something mathematicians had struggled to improve for years.
If you're interested, I can also explain how the AI actually searches the graph space (it’s a fascinating mix of evolutionary algorithms + combinatorics + SAT solving).
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