April 30 2018 RRG Notes

Disguised Queries

Imagine that you have a job sorting objects into two bins
- Blue, egg-shaped objects go into the “blegg” bin
- Red, cube-shaped objects go into the “rube” bin
Once you start working, you notice that bleggs and rubes differ in ways other than their color and shape
- Bleggs are furry, whereas rubes are smooth
- Rubes are hard, whereas bleggs flex slightly to the touch
- Bleggs are opaque, whereas rubes are translucent
One day, you encounter a strange object
- Color is halfway between red and blue, i.e. purple
- However, this object shares all of the other characteristics of a blegg (egg-shaped, furry, opaque, etc)
- So is it a blegg or not?
You then find out that the reason bleggs and rubes have to be separated is that bleggs contain vanadium and rubes contain palladium
So is that the real difference between bleggs and rubes?
- What if 2% of the time, a blegg contains palladium instead of vanadium?
Asking whether something “really” is a member of a category is a stand-in for some other question
Categories are lines we draw in thingspace
Arguing about categories is useless unless you’re using those categories for something
Objects don’t suddenly change their characteristics when we recategorize them

Suppose we’re creating a neural net to classify bleggs and rubes
A naive neural net would represent all of the characteristics of bleggs and rubes as nodes and would have links from every node to every other node
When this neural net sees something that’s purple, but still egg-shaped and furred, it will still successfully classify it as vanadium-containing
The categories of “blegg” and “rube” are implicit, emergent properties of the neural network, rather than explicit nodes
However, this neural net has a few problems
- Large number of connections required - every node has to be connected to every other node
- Takes a long time converge - signals have to propagate forwards and backwards before the neural network converges on a judgement
A better neural net looks like
This neural net has an explicit node for the blegg/rube distinction
As observations come in, they activate nodes which feed into the explicit node, pushing it above or below the activation threshold necessary to declare something a blegg or a rube
This neural net is much more efficient and converges to an answer much more quickly than the previous naive neural net
Because of this, it’s probably a better way to model how our brains actually handle categorization problems

The second neural net above gives us an intuitive answer for why we get into arguments over definitions
Most of the time, input from the world is unambiguous - something is either a dog or a cat, and central node either activates or doesn’t
We run into problems when there’s ambiguous input - the central node is either just below or just above the activation threshold
This results in the feeling of uncertainty about whether an object “truly” fits into the category we have assigned it to
If our minds were constructed like the first neural net above, once we’d observed the physical characteristics of an object, we wouldn’t feel like there were any questions left to ask

Even if ancient Hebrews had perfect knowledge of animal genetics and phylogenics, they still wouldn’t be wrong to call a whale a fish
The distinction that mattered to Hebrews was not a matter of evolutionary ancestry, but rather, “Do I need a boat or a horse to catch it?”
Definitions are only “correct” or “incorrect” insofar as they help us achieve some other goal
In this definitions are much like the borders between countries - there is no such thing as a “correct” border; every border is the result of a particular set of political tradeoffs
There is nothing in the world that dictates which characteristics you should use to define your categories - the only thing that matters is whether dividing the world by those categories is useful towards the goal that you wish to achieve
This applies equally to questions of gender or mental illness
- There is nothing forcing us to use particular physical or chromosomal characteristics to distinguish between male or female
- There is nothing forcing us to use particular behavioral charactistics to distinguish between normal behavior and mental illness
We should draw boundaries such that they’re useful for the goals that we’re trying to accomplish
If these boundaries are no longer useful for our goals, we should (re)draw them differently so that they become useful

Words don’t have meanings; we assign words meanings in order to communicate
When we hear a word, our brains will automatically translate that word into its associated meaning
Most of the time this works very well, and is the reason that we can communicate at all with speech or text
However, when two people use a word differently, confusion occurs because the same word points to different concepts in each person’s mind
This results in arguments about whether an object is “truly” part of a particular category
We forget that categories are part of the map, not the territory

Is it a sandwich?