My Grandfather Thought He Solved a Cosmic Mystery

For every possible input 0 to X you need to map to a different 'compressed' format. So, if you want to handle every possibility then some of your compressed versions need to be as long if not longer than the original version. That's not a problem if their is some bias in how your generating the data. Just map the more common versions to shorter encoding and you get a useful compression even if sometimes it makes things worse on average their is an improvement. But, with unbiased random data you can't chose which subset is more likely because every version is equally likely. Which is why it does not work.

They always think they have a big idea. It's never some minor correction to a big theory, which a PhD would be happy with (as long as it's major enough to be publishable); no, it's Shatter The Foundations or nothing. Therefore, they're being done out of their fame and fortune by some grand conspiracy, which, in itself, proves how important they are: If they weren't right, They wouldn't be conspiring against them, now, would they? That mindset certainly sells books, and helps on the lecture circuit, too.

I'm sure there are some honest crackpots, but I wonder how honest you can be when you come upon a bit of well-accepted physics you can't understand or simply don't like, and conclude that everyone else is wrong, and you're the only one who's correct.

If a person can't be convinced with real evidence, that is the road to crack-pottery.

Typically there's some agreement with a difference of either an underlying core axiom or some other tradeoff that the two people are weighing differently.

Pointing out the pieces you agree on helps the other person relax a little and open up when thinking about their position.

One of the human failure modes that I witness on a regular basis is that people fail to separate "I hear/understand you" and "I agree with you" within their own heads. People have a tendency to assume that what they find convincing will be similarly convincing to another. As a result, if it's not convincing to another, this other person must not understand it properly and must just need to be educated on the subject. Or, more cynically, they aren't paying attention because they don't understand the importance of the work.

My current operating hypothesis is that vanishingly few people are genuinely interested solely in ideas. Almost everyone has some ego at stake. Being told that your baby is ugly, no matter how kindly, compassionately, or empathetically it is done, is rarely a positive experience. This is where people like Dale Carnegie come in.

Beyond the emotional aspects of it, there are other issues. It can be incredibly labor-intensive to delve deeply into a paper and determine how right or wrong it is. If it's wrong, it's even more work to understand precisely where and how it is wrong, and then give the kind of feedback a hypothetical egoless author genuinely interested solely in ideas would like. This can be a great deal to ask, unpaid, of people who have other things they would like to be doing. This is doubly true when most papers are patently wrong in some obvious way and the painstakingly handcrafted feedback unlikely to be taken up in the manner an idealist could hope for. I'm sure you have a way to handle this with the art of listening, and I'm just not seeing it. Can you help me understand?

Again, you're completely right. It can definitely help to separate the ideas of understanding and agreement, and reasonable people interested in ideas will handle this gracefully! There just might be some room for nuance and perhaps a careful consideration of costs and burdens might be in order.

without commenting on importance, novelty, truth ... he explains clearly the (conditional) probability functions and performs substitutions i.e. deriving conclusions.

In principle, someone could be both right and incomprehensible, but there's no way forward unless one can get some people to both understand and agree with you. Even then, you could end up with one faction thinking it is on to something profound, while another thinks they are mistaken, as is happening with Integrated Information Theory at the moment.

I don't think this necessarily holds. I'd need to look at studies, but I feel that the more time you've invested into something, the worse rejection is, sound mind or not. And this would be compounded if you get the feeling the other person isn't even trying to understand you and your point of view.

"Thank you for developing a good approximation to the trisection of an angle! It has an average error of only 0.1 percent, according to this computer analysis of all angles from 0 to 180 degrees in steps of three. It compares favorably with past approximate trisections developed by X, Y and Z that work as follows..."

The "Grandfather" in the story argued that we can consider the problem specified if we assume that "the set of all distinct possible states" are uniformly distributed -- which is reasonable and correct when solving problems in quantum mechanics but unreasonable in ordinary everyday situations.

Thinking along those lines, you can construct a set of all possible concentrations: (0 wine particles, N water particles), (1 wine particle, N-1 water), (2, N-2), ... (N, 0). That led to my x/(1-x) formulation, which has the advantage of avoiding the paradox as stated, but I would not argue it's a well-founded result.

The main lesson is that the Principal of Indifference is "not even wrong". (It's nonsense.)

If you want to form an opinion about Freud please do research what psychological community thinks about him and why. Basically, "he was asking interesting questions and giving wrong answers but we remember and value him for the questions."

> I know absolutely nothing about psychology except I read some Freud.

For me it sounds like "I know absolutely nothing about piloting aircraft except I read some notes of failed inventor that tried to build a flapping wings plane before Wright brothers flew, but noone remembers his name because aviation is not psychology."

Or "I know exactly nothing about solar system except I read some Ptolemy."

If you are interested in Freud, read Freud. If you are interested in psychology read something way more modern.

What I think distasteful is that psychological society didn't distance their trade from Freud enough and in 2018 you were under the impression that reading Freud counts in any way towards learning psychology.

And to address your more general point. How can you know if Freud is the crank or I'm the crank without knowing anything about the subject and without any interest in the subject?

You can't but it's ok since you have no interest. And if you are pressed against the wall you are safer with opinion of majority. Not even majority of psychological community. Just majority of people. Freud was famous so he can't be that bad.

From some googling I did find this: https://arxiv.org/abs/quant-ph/0310073

To answer your question: in some cases, transferring probabilistic reasoning about discrete states to continuous states, or vice versa, is sort of trivial. But sometimes it becomes somewhat controversial, and often this is because it's unclear how the scale of information maps onto the scale of data, to put it murkily. When it's discrete, you know your observations have specific possible values, which in itself is a chunk of information. But when it's continuous, you have an infinite range of values, and what constitutes "indifference" can be unclear.

Think of a scale (like a kitchen or bathroom scale), for example. The scale will have a certain accuracy within a certain range, and as you go further outside that range, the accuracy will decrease further and further. So, to make an analogy with the water-and-wine paradox, let's say I tell you "here's this container of walnuts, that could be anywhere from 0 to 100kg. What's the probability its mass as measured on this scale is in a certain range?" What would be adhering to the principle of indifference? You could argue it would be a uniform distribution over the numbers from 0 to 100, but you could also say it's somehow uniformly distributed over the distinguishable units of the scale, which will not be uniform from 0 to 100 because the meaningfulness of the scale's numbers will be compressed in its most accurate range, and stretched in its less accurate range, and there will also be issues with machine precision, etc. If you were counting walnuts though, you've kind of implicitly fixed the scale to the nonnegative integers, and assumed your ability to count doesn't get fuzzy at some point. So you assume uniformity on one scale is uniformity on another.

E.g., if you think of Jeffreys prior as being one scaling of indifference, even with a Bernoulli variable, indifference isn't necessarily scaled as a uniform: https://en.wikipedia.org/wiki/Jeffreys_prior.

I think this paradox involves (along with maybe being underspecified or poorly posed) somewhat related information-scale mapping issues, about how you define uniformity and what your "possibility space is" to be sort of Jaynesian about it.