Thread by @paraschopra

1/ A thread with thoughts on measurement.

Examples of questions I'll explore: do inherent measures and properties of a system exist? What does this imply about science's pursuit of absolute truth?

2/ Measures and properties of a system are always in the context of:

- how you define a system? what boundary do you put on the system?
- what does that defined system do to other things in the world?

3/ For example, think about what does it mean to say that a particular person has an IQ of 120.

4/ First, we are implicitly putting a boundary on an individual to study it. Perhaps intelligence has contributions from culture, food, parenting, etc.

But by ascribing IQ to a person, we've made clear that our boundary is what constitutes a person.

5/ Second, the measure IQ carries information not just about the person (system in question) but how it was measured (a particular test).

And the method of measurement depends on interaction of system with the world.

6/ So a measure is the property not just of the system, but of the world.

Remember: whenever we describe a property or measure of a system, we're coarse-graining it at some level.

7/ This means that things there's no such thing as inherent 'intelligence', 'beauty', 'quality'.

Your measurement depends on how you measure those things. Change your definition and you change the number.

8/ So far all what I've said is obvious. What I'm interested in exploring is:

- If there are infinite ways to measure an infinite properties of a system that can be defined in an inifinite number of ways , why do some combinations get picked over others?

9/ - What about fundamental properties like mass, charge or volume?

10/ My hypothesis for the first question is that measures get picked/prioritized by their usefulness to the measurer.

Armies use IQ because it measures precisely the properties of a person that's useful when it comes to being a soldier.

11/ Ultimately, IQ may be implicitly measuring something else entirely - perhaps ability to sit through exams, or pattern matching, or a mix of many such properties.

Hence, the behavior of the person (system) under measurement conditions is what defines the measurement.

12/ For IQ, a catch-all phrase 'intelligence of a person' is used but ultimately IQ is not just a measure of a person, but the measurer's (army's) goals / objective fo what it wants to do.

13/ A measure survives over a period of time because it's useful.

So, re-emphasizing my earlier point, usefulness trumps truth/accuracy (whatever 'truth' may mean):

https://twitter.com/paraschopra/status/1074157672587517952

14/ Are fundamental properties like mass, charge also relational?

Ultimately, nobody knows what 'stuff' is everything made of and what are fundamental properties. We know an electron's mass by what effects does it have on the world (measurement apparatus).

15/ Charge and spin as properties are also coarse graining at some level because they help us better predict in our scientific theories. They're useful measurements.

I'm increasingly of the opinion that usefulness is perhaps a primary concept and truthfulness is secondary.

16/ That's it. Hope you enjoyed the musings :)

I'm collating all my Twitter Threads (including this one) on this page: invertedpassion.com/twitter-thread…

17/ Actually, one important point I missed. The relativeness of measurement / representations has direct impact on machine learning.

18/ Representations of inputs make sense only in context of goal.

Given an input image of cow, the latent representations learned for that input are very different if the task is of classification than if it is of image captioning or removing background.

19/ I find it fascinating because this means unsupervised learning - learning without a goal makes no sense.

Even pixels of an image make sense in the context of helping us - humans - recognize an object as a dog or something else.