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DanArmak comments on Privileging the Question - Less Wrong
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If I can solve planetary motion, I will be famous and professionally respected. I will feel great about myself, rich noblemen will want to become my patrons, and I will be appointed to prestigious and lucrative posts like President of the Royal Society or Master of the Mint. I will be forever remembered as one of the greatest scientists in all of history!
That might count as "signaling".
What exactly counts as "signalling"? I started to write down a definition, but I think it's better you give yours.
The colloquial definition is "Useless but impressive and flatters my vanity".
The probabilistic definition is "Observable thing X signals quality A means P(A|X) > P(A)".
The economic definition is "Alice signals P to Bob by X if the net cost of X to Alice is outweighed by the benefits of Bob 'believing' A, and X causes Bob to 'believe' A even when Bob takes in to account that Alice wants him to 'believe' A." (note 'believe' A means 'act as if A were true'.)
Useless to whom?
Newton was respected for coming up with useful theories and natural science, not just pure philosophy or non-applied math. You could maybe argue that his work was rarely useful to him personally, so he only did it as "signalling" to get respect from others to whom it was useful. But under that theory, any division of labor where people are paid money for their work which is only useful to others would be called "signalling".
That's true: that Newton came up with good theories in the past is evidence he'll come up with more good theories in the future. It signals his quality as a scientist.
But this is a good thing (as opposed to the usual negative implied connotations of "mere signalling"). And the reason it's a good thing is that his scientific work was actually useful, so it's a good thing others could identify this and reward him to make him do more useful work.
That's just saying "people will choose to signal if benefits exceed costs". It's true, but it doesn't explain to me the original statement:
Which says "signalling' in this instance is something that motivates people in the absence of things being useful in their own right.
Using my theory of planetary motion, I will be able to STOP THE EARTH FROM CRASHING INTO THE SUN.
But you killed the gnomes and the fairies!
Because they did not obey my scientific theories, they went on to CRASH INTO THE SUN!
Even without a coherent theory of planetary motion, we can assign a very low probabiliy to the earth crashing into the sun simply on the basis that it hasn't yet.
...that is exactly the sort of judgment which requires some sort of theory. Every day, trillions of things happen which have never happened before. Never in the history of the universe has this comment been posted to LW!
Well, a couple days ago, we could reasonably have assigned a pretty low probability to that exact post being made today.
New things happen all the time, but without a model, we can't assign much likelihood to any specific new thing happening at any particular time.
Without some kind of model, you can't assign any probabilities period (.)