PeterDonis said:
So you basically think that waiting around for someone else to do this for you--which could take days, or weeks, or months, or might never happen at all--is a better option than just looking up the papers for yourself and reading what they say? And you think that taking what other people say at face value about anything you don't understand yourself is a better option than trying to understand it yourself?
For the record, I think you are showing very bad judgment if that really is your preference.
I do look up the papers for myself and read what they say. I just don't have the level of mathematics required to understand the math content. I have started to re-learn high school mathematics, but it may be a while before I'm at the level where I can answer questions like these for myself. That is why sites like this one can be a beneficial aid to the learning process because there are, or at least appear to be, members on here who do understand that side of things.
As I said, currently, I am in a position where I have to take at face value the statements people make, just as I have to take at face value plenty of other facts about the world around me, because it simply isn't practically possible to learn everything about everything. But, taking things at face value doesn't simply mean believing that they are an accurate representation. It involves cross-referencing them with other statements from other members and other sources, such as the authors of papers themselves.
If 99% of the sources one encounters all say effectively the same thing, then there is a higher likelihood that what they say is an accurate representation. It is possible that there is a giant conspiracy being perpetrated where all of these people are deliberately trying to mislead everyone else. So yes, taking things at face value is predicated on two assumptions:
1) Those making the statements are not engaged in a giant conspiracy
2) Those making the statements are knowledgeable enough to give an accurate representation of the topic under consideration.
Once you have these two assumptions you can then learn from other people's expertise.With regard to the mathematics in particular. As mentioned, the mathematics encodes assumptions and fact
about the real world. A good example of this is Einstein's 1905 paper where he uses the example of a train pulling into a station to demonstrate the idea of "simultaneity", referring to a wrist watch. Or, as Leonard Susskind demonstrates in the
the Theoretical Minimum, when he explains how to encode dynamical laws in equation form:
He takes a real world object i.e. a coin which can be in either of two states, H or T, and gives an example of a dynamical law. He then demonstrates how to write this in equation form. But, the equation always describes the real world scenario and to
interpret the math, we must refer back to a real world scenario.
The same is true for the use of calculus to calculate rates of change or any other branch of mathematics, which purports to tell us things about the natural world. First, assumptions/facts about the natural world are encoded in mathematical form, then the mathematics can be manipulated (more precisely than ordinary language) to draw conclusions and make predictions about the natural world, but ultimately, the natural world is the arbiter of truth. If the observations made in the natural world don't match the predictions of the mathematics, then it is the mathematics that has to change. Similarly, to
interpret the mathematics, is say what it tells us about the natural world.
Take the theory of relativity for example. The mathematics by itself doesn't tell us anything. It's just symbols. Only when it is related back to the natural world do the symbols have meaning. For the theory to make predictions about the natural world the mathematical symbols must be connected to phenomena in the natural world. This is how we determine if the mathematics is accurate.
There is also a conversation we had previously about
the Block Universe. Some have argued that the Block Universe is the only way to interpret the mathematics of relativity, while you pointed out that this isn't necessarily true. You demonstrated that it can be interpreted in the context of presentism or in the manner outlined in your insight article. The mathematics doesn't tell us any of this because it is compatible with all of them. To develop a fuller picture of what the mathematics tells us about the natural world, we have to interpret it in terms of the natural world.Mathematics is one of the single most effective tools man has ever invented. It has allowed us to investigate ideas more efficiently than ordinary language. But, it does this by taking phenomena in the natural world, which
can be described in ordinary language, albeit technical, and encoding it in the symbols of mathematics. By manipulating the math we can then analyse situations more effectively and efficiently. We can make predictions about future observations. But, those predictions are about observations in the natural world and
can be described in ordinary language.
It is the first and last steps in that process that I have been enquiring about.
PeterDonis said:
Whether I do or not is irrelevant. You are the one who should be able to precisely describe what you mean. I should not have to guess or fill in blanks for you. Particularly about a concept that is so basic that anyone who wants to have an intelligible discussion about relativity should be able to precisely describe it.
At least, that's my preference. Yours is evidently different. Anyone else reading this thread is welcome to respond according to your preference if they wish.
I'm not sure if you are familiar with the concept of a
steelman? It's where you take the strongest possible interpretation of the other persons statement.
Either way, it serves to demonstrate the point I have been making when you say that anyone who wants to have an intelligible discussion about relativity should be able to precisely describe [the concept]. The concepts can be discussed using ordinary language, albeit technical.
I was trying to find out precisely what Bell meant and what assumptions about the natural world he had encoded in his theorem; I was inquiring about the precise statements made by Bell and others about those assumptions. Again, I was looking at the first and final steps in the process. Given the deficit in my mathematical ability, I am in a position where I have to take it at face value what those who are more familiar with the mathematics tell me.One conclusion that can be taken from this discussion is that it's not necessarily the case that Bell's statements about the assumption of free will or free variables in his own theorem, and the statements of the others, are inaccurate, it's that neither you nor I are not familiar enough with the mathematics to say whether they are or not.
We could always take Bell at face value and work on the assumption that he knows what he's talking about.