unprompted/Notes/art-of-doing-science.md

## Rough Notes
- As the number of dimensions increases, the volume of the sphere approaches 0. Not that this is remotely grounded in reality, resonates with the gut-instinct that the multi-dimensional possibilities exist as virtually non-existent bundles at a vanishingly small scale.


## 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?