Polytopos

Polytopos' Comments

Mathematical Intuitionism and the Flow of Time

Thanks for your comment. My replies are below.


"so Gisin's musings... are guaranteed to be not a step in any progress of the understanding of physics."

What is your epistemic justification for asserting such a guarantee of failure? Of course, any new speculative idea in theoretical physics is far from likely to be adopted as part of the core theory, but you are making a much stronger claim by saying that it will not even be "a step in any progress of the understanding of physics". Even ideas that are eventually rejected as false, are often useful for developing understanding. Gisin's papers ask physicists to consider their unexamined assumptions about the nature of math itself, which seems at least like a fruitful path of inquiry, even if it won't necessarily lead to any major breakthroughs.


"mathematical proofs are as much observations as anything else. Just because they happen in one's head or with a pencil on paper, they are still observations."

This reminds me of John Locke's view that mathematical truths come from observation of internal states. That is an interesting perspective, but I'm not sure it an hold up to scrutiny. The biggest issue with it seems to be that in order to evaluate the evidence provided by empirical observations we must have a rational framework which includes logic and math. If logic and math themselves were simply observational, then we have no framework for evaluating the evidence provided by those observations. Perhaps you can give an alternative account of how we evaluate evidence without pre-supposing a rational framework.


"The difficulty of calculating a far-away digit in the decimal expansion of pi has nothing to do with pi itself: you can perfectly well define it as the ratio of circumference to diameter, or as a limit of some series"

I agree with this statement. I think though it misses the point I was elaborating about Brouwer's concept of choice sequences. The issue isn't that we can't define a sequence that is equivalent to the infinite expansion of pi, I think it is rather that for any real quantity we an never be certain that it will continue to obey the lawlike expansion into the future. So the issue isn't the "difficulty of calculating a far-away digit" the issue is that no matter how many digits we observe following the law like pattern, the future digits may still deviate from that pattern. No matter how many digits of pi a real number contains, the next digit might suddenly be something other than pi (in which case we would say retrospectively that the real number was never equal to pi in the first place). This is actually what we observe, if we are to say measure the ratio of a jar lid's diameter to it's circumference. The first few digits will match pi, but then as we to smaller scales it will deviate.


"...the idea that Einstein's equations are somehow unique in terms of being timeless is utterly false"

I made no claim that they are unique in this regard.

How effective are tulpas?

I agree that the term mindfulness can be vauge and that it is a recent construction of Western culture. However, that doesn't mean it lacks any content or that we can't make accurate generalizations about it.

To be precise, when I say "mindfulness meditation" I have in mind a family of meditation techniques adapted from Theravada and Zen Buddism for secular Western audiences originally by Jon Kabat-Zinn. These techniques attempt to train the mind in adopt a focused, non-judgemental, observational stance. Such a stance is very useful for many purposes, but taken to an extreme it can result in de-personalization / de-realization and other mental health problems.

For research to support this claim I recomment checking out Willoughby Britton's research. Here are two PDF journal articles on this topic: one, and another one.

How effective are tulpas?

I agree about mindfulness meditation. It is presented as a one-size-fits-all solution, but actually mindfulness meditation is just a knob that emphasizes certain neural pathways at the expense of others. In general, as you say, I've found that mindfulness de-emphasizes agential and narrative modes of understanding. Tulpa work, spirit summoning, shammanism, etc. all move the brain in the opposite direction, activating strongly the narrative/agential/relational faculties. I experienced a traumatic dissociative state after too much vipassana meditation on retreat, and I found that working with imaginal entities really helped bring my system back into balance.

How effective are tulpas?

I have often thought that the greatest problem with the tulpa discourse is the tendency there to insist on the tulpa's sharp boundaries and literal agenthood. I find it's much more helpful to think of such things in terms of a broader class of imaginal entities which are semi agential and which often have fuzzy boundaries. The concept of a "spirit" in Western magick is a lot more flexible and in many ways more helpful. Of course, this can be taken in an overly literal or implausibly supernateralistic direction, but if we guard against such interpretations, the idea of spirits as agentized meanings is very helpful.

How is this practically useful? For me it comes down to leveraging the huge part of the brain which works in terms of agency and narrative. Learning how to work with imaginal entities opens up a vast amount of general processing power that would otherwise be domain specific.

Of course, all the warnings that people have said about mental health and possible psychosis and dissociation are genuinely worrisome. So embarking on these sort of practices should be undertaken with quite a lot of care.

Why hasn't the technology of Knowledge Representation (i.e., semantic networks, concept graphs, ontology engineering) been applied to create tools to help human thinkers?

Thanks to the comments and discussion, I was motivated to do more research into my own question. What I've found is that there have been some attempts to use semantic technologies for personal knowledge management (PKM).

I have not found evidence one way or the other as to whether these tools have been helpful for knowledge discovery, but they seem promising.

The main tool that would be accessible to the average user is Semantic MediaWiki, this is an extension to Wikipedia's popular MediaWiki software that adds KR functionality based on semantic web technologies.

Here is an article about how to set this up for PKM.

PDF Journal article Semantic Wikis for Personal Knowledge Management

-This article does a good job outlining a general theory of how to build a semantic knowledge application for PKM. The arguments are not tied to a specific software implementation.

PDF Journal article Learning with Semantic Wikis

-I haven't read this article yet, but from the abstract it sounds generally useful

Why hasn't the technology of Knowledge Representation (i.e., semantic networks, concept graphs, ontology engineering) been applied to create tools to help human thinkers?

Interesting, can you give some examples to illustrate how causal/Bayes nets are used to aid reasoning / discovery?

I see merit in the idea that semantic networks may focus too much on the structure of language, and not enough on the structure of the underlying domain being modelled. As active thinkers, we are looking to build an understanding of the domain, not an understanding of how we talked about that domain.

Issues of language use, such as avoiding ambiguity, could sometimes be useful especially in more abstract argumentation, but more important is being able to track all of the relationships among the domain specific entities and organizing lines of evidence.

Why hasn't the technology of Knowledge Representation (i.e., semantic networks, concept graphs, ontology engineering) been applied to create tools to help human thinkers?

Good hypothesis, here is why I don't think it's likely to be true.

It seems to me that when humans make explicit arguments with written language, we are doing a natural language form of knowledge representation. In science and philosophy the process of making conceptual models explicit is very useful for theory formulation and evaluation. i.e., In conceptual domains, human thinkers don't learn like today's neural nets, we don't just immerse ourselves in a sea of raw numbers and absorb the correlations. We might do something like that on the perceptual level, but with scientific and philosophical thought, we are able to abstract over experience and explicitly formulate hypotheses, theories, and arguments. We name patterns to form concepts, and then we reason about these concepts. We make arguments to contextualize and interpret the significance of observations.

All of these operations of human thinking involve a natural language version of knowledge representation. But natural language is imprecise and it doesn't scale well. It is transmitted through books and articles that pile up as information silos. I'm not saying we can or should eliminate natural language from intellectual inquiry, it will always have a role, but my question is why haven't we supplemented it with a formal knowledge representation system designed for human thinkers.

Why hasn't the technology of Knowledge Representation (i.e., semantic networks, concept graphs, ontology engineering) been applied to create tools to help human thinkers?

Hi Said. I'm new here, would you mind explaining what a sidebar is, maybe providing a link or instructions to find said sidebar? Thanks.

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What is your Personal Knowledge Management system?

I use Notion.so. I mostly use it like a wiki, but I find the rich formatting and easy move-ability of the blocks to be helpful. I also use the database features to collect notes for ongoing projects, using it more like a journal. Notion is slow on mobile, but I find that taking the time to transfer bookmarks and insights to Notion helps consolidate them.

For organizing ideas that have a temporal component, I use preceden.com timeline. This is great for keeping track of books I've read and for medium and long term planning.

For longer thoughts and writing I use Google docs. I use Google Drawings for mindmaps and conceptual diagrams. I then link to the docs and drawings from Notion.

For PDF articles I use Notability on my iPad. This has excellent highlighting and note-taking features.

For ebook reading and organization on the iPad, I use Kybook.

For video lectures Youtube playlists, with youtube-dl gui for offline viewing.

I have been wishing for a long time for a fully integrated solution, but each tool has it's strengths and weaknesses.

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