Dear Israel,
Thank you for the reply. While, as you have seen, we have many points of agreement, your answer developed well the point of disagreement. I am fully for intuition and for pictorial explanations. But I have the feeling that we use different definitions of intuition, and here may lie the difference. For example, mine include bad and god variants of intuition. Intuition can fail us, and can help us. When you say "intuition", you seem to refer to only the good one: it is always correct, and if it is not, the cause is external. You say people's intuition was wrong because they did not have enough information, or because religion influenced them. Therefore, information is obtained by other means, which are experiments and logic. After gathering information about the solar system, it is not hard for intuition to admit that the Earth is moving. So, this kind of intuition seems to be useless, because always states what is believed at that time. The second thing that you say distorted intuition was religion. Well, religion did not come from math or from experiment, it came from people's feelings that the loved ones and us should not really die, that it has to be a divine justice to repair the injustice in the world, etc. In other words, from intuition.
If some pope during Copernicus's or Galileo's time had the intuition build on the incomplete knowledge at that time, that the Earth is not moving, how could Galileo appeal to pope's intuition to explain that in fact it is moving?
Similarly, if in the times of Einstein people rejected relativity and tried to explain the same phenomena by using the ether theory, which their intuition said it is right, should Einstein give up and explain everything in terms of the ether? Maxwell's equations are so simple, but trying to explain them by ether or gear mechanisms is so complicated. SR is so simple, define just by a 4x4 matrix. GR is also so simple, just the geometry of a curved 4D space. I don't say they are complete, but much simpler than any alternative tried so far, based on ether etc. And when you train your brain in that math, intuition grows, and you have indeed an intuition for them. It is not true that nobody understands 11D or landscapes. Also, it is half true that nobody understands QM. Some understand it better than others. While I have some inside information that many quantum theorists write articles in the plain formalism of QM, they use "secretly" one or another interpretation of QM. They use the intuition, and get new results, and write them in a pure formal manner. Also, in the most abstract math, people don't derive the results by making blind calculations, which they don't know where will lead. They use simplified models to grasp the ideas, then they apply to more complex and more general structures, and generalize, and get the results. Sometimes, in geometry or GR, they calculate using index notation, then replace it with the modern notations. The most abstract branches of math, and the most difficult branches of physics, advance, even those 11D, because people build their intuition in parallel to technical abilities. Those who are too good to use models and intuition, in general are less successful. Now, what I said so far is based on anecdotal evidence I collected in private conversations, guided by some intuitions I have about the creation process in science. It is not backed by a study or at least a poll (you may remember that recently at least two polls are made about how physicists see QM, and the polls are very contradictory).
Often, intuition in one domain is useful to solve problems in another one. I am thinking at imports from statistical mechanics in QFT, or at the imports from condensed matter. You said "Giving the mathematical analogies of these systems with the quantum vacuum, some physicists have suggested that the vacuum could be indeed a quantum liquid, i.e., a state of condensed matter [17]." I would like to emphasize in what you said "mathematical analogies". The question is, after using an analogy like this, when we want to learn about quantum vacuum, should we also learn condensed matter physics? The analogy is useful to make discoveries, and to explain, but at some point, the analogy may be no longer needed. Even if we want to rewrite everything based on common sense, condensed matter physics also is far from the common intuitions of the lay persons. Intuition has to develop in parallel with the more technical parts. It should not be a Procustian bed to cut the math to fit in our Lego/Meccano/Minecraft-based intuition.
My intuition tells me that we essentially agree, and the discussion was just to clarify possible misunderstandings :)
Best regards,
Cristi