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unprompted/Notes/art-of-doing-science.md
Stephen Donahue 234f3697f6
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[notes] happy idiots
2026-04-20 03:56:36 +00:00

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## Rough Notes
## Questions
### Are people more alike, or different than machines?
- Since I'm just talking to myself here, I'll pin that as a similarity, more than a difference
- Machines (I'm specifically thinking of computers) spend a great deal of time generating and handling internal messages and signals.
- It's worth reiterating that networked communication came later, and before that time, the bulk of external communication was with a single user through some narrow interface
- Machine's don't belabor the unoriginality of their output. They just produce prodigious amounts of structured data. A great deal of it mind-numbingly repetetive.
- So here I'd say that more effective people, less concerned or completely indifferent to the novelty of their thinking,
- but rather focused on the appropriateness, given the context, or the richness of taking an idea off the shelf and applying it in some new way.
- "The Terroir"
- Less effective people are constipated, preoccupied with the wrong evaluation.
- Ideas get propagated because they're reactive
- You can have truly original ideas that are deranged and go nowhere (maybe they just rattle inside your head.)
- But the ideas that get repeated, passed on, have a "contageous" quality that doesn't burn out
- They're enticing. Why?
- A lot of marketing - you'll like what you're told to like
- But that starts to feel circular:
- like what you're told to like
- told to like what people like
- We might try on an idea, walk it around a bit
- But I don't think marketing pressure alone can sustain it
- Needs some dose of intrinsic appeal
- But even that acclimation can come from repeated exposure.
- So again, the things we want are the things we've been routinely exposed to by one factor or another
- Some intrinsic value (or potential - does that even exist?)
- Some machines are serviceable, others are not. In general, people are only serviceable by other people with specialized knowledge and training. Same goes for a lot of integrated circuits I've met, CPU dies and the like.
- So this isn't a great defining quality for machines. It's a better one for people
- A better way of phrasing it, to avoid trending into irrelevance:
- some machines exhibit modularity. Parts can be swapped out for compatable ones.
- But then, that sounds closer to people. Maybe we're not hot-swappable, but we face compatability issues. Blood types, organ donations. Could maybe stretch it to overlap with the parts metaphor, where maybe a badly compatible part could be swapped in disasterously.
- So the similarities and differences have more to do with an attitude than an absolute.
- I wouldn't know how to prove that there will always be counter-examples, or alternative perspectives for every argument made for one camp or the other.
## Quotes
## Definitions
### Stirling approximation of `n!`
- `ln(n!) ~= n * ln(n) - n
- or `n! ~ sqrt(2*pi*n) * (n/e)^n
- why does a circle appear?
- logarithm rule
1. let a = e^p s.t. ln(a) = p
2. let b = e^q -> ln(b) = q
3. a * b = e^p * e^q = e^(p + q)
4. ln(a * b) = p + q = ln(a) + ln(b)
5. qed motherfuckers
- `ln(1) = 0`
### Power Rule
(u * v)' = u'v + uv'
(x^2 * sin(x))' = 2x * sin(x) + x^2 * cos(x)
### Integration by parts
int((u*v)') = u*v = int(u' * v dx) + int(u * v' dx)
### Thinking
- WTF is thinking, anyway?