Over the last few months, I've been developing an unorthodox perspective on entropy [1] . It defines the phenomenon in much more detail, allowing for a unification of all forms of entropy. It also defines probability through the same lens.
I define both concepts fundamentally in relation to priors and possibilities:
- Entropy is the relationship between priors and ANY possibility, relative to the entire space of possibilities.
- Probability is the relationship between priors and a SPECIFIC possibility, relative to the entire space of possibilities.
The framing of priors and possibilities shows why entropy appears differently across disciplines like statistical mechanics and information theory. Entropy is not merely observer-dependent, but prior-dependent. Including priors not held by any specific observer but embedded in the framework itself. This helps resolve the apparent contradiction between objective and subjective interpretations of entropy.
It also defines possibilities as constraints imposed on an otherwise unrestricted reality. This framing unifies how possibility spaces are defined across frameworks.
Yes. There are different concepts called 'entropy', sometimes merely because their mathematical formulation looks very similar.
It means different things in different contexts and an abstract discussion of the term is essentially meaningless.
Even discussions within the context of the second law of thermodynamics are often misleading because people ignore much of the context in which the statistical framing of the law was formulated. Formal systems and all that... These are not general descriptions of how nature works, but formal systems definitions that allow for some calculations.
I find the study of symmetries by Noether much more illuminating in general than trying to generalize conservation laws as observed within certain formal models.
Whenever there is an entropy, it can be defined as
S = - sum_n p_n log( p_n )
where the p_n is a probability distribution: for n = 1...W, p_n >= 0 and sum_n p_n = 1. This is always the underlying equation, the only thing that changes is the probability distribution.
Ah maybe you mean in the temporal sense? Yea that could be a useful shelling point. I was thinking spatially, obviously insects can't fly to the moon to reproduce .
Ambiguity is an intrinsic quality of language. The first words that an infant learns are exclusively learned through ostensive definitions (defining by pointing). This implies that the meaning of those words is fundamentally different to each of us, as it's founded on our phenomenological experience and not through the dictionary.
Further words are learned to combine previous definitions and more ostensive definition, so ambiguity is carried on.
Lojban does not eliminate the ambiguity of the meaning of the words, but the ambiguity of its syntactical structure.
To me, the ambiguity of language, and the impracticality to change the meaning of words are the fundamental issues preventing humans to enhance the innate cognitive abilities, and the root cause of most human conflicts around communication.
Any profession and culture has its own jargon, this enables them to express the particular quality of their reality with much more accuracy than common language.
So, instead of trying to build a shared language, what we can do is to create a personal Language for each of us. Not for the purpose of communication, but for the purpose of improving our reasoning and internal model of the world, so we can describe and make sense of our particular reality with much more accuracy.
I've been dedicated to building "Interplanetary mind-map", a tool that supports making your language by making your meaning more explicit. [0]
At the same time, I've been using a prototype of it, to build my personal Language. You can browse into each word and see my particular understanding of it. [1]
I think going from the difference in environment in learning first words to the meaning of those words being fundamentally different for everyone is a non sequitur.
Specifically when not defining the ambigous concept „meaning“ and without sketching the assumed mechanism by which they are learned and turned into language.
Lojban could have gone further to eliminate logical ambiguity, allowing monoparsing from sentence to an explicit statement in a framework of computational semantics (e.g. Davidsonian event semantics). That Lojban did not was one of its great failings.
A more relatable example to me is with chocolate bars.
A 85% chocolate has 3 times more sugar than a 95% chocolate.
I wonder the world-wide impact in people health if they advertised the ratio in terms of sugar instead of cacao.
This is fascinating... I've been working on an extremely similar protocol Interplanetary mind-map [0] for about 5 years. I'm surprise I've never seen Noosphere before.
It has the exact same topology, on top of IPFS and IPLD, and its also motivated as a tool for thought and aiming to enable transclusion among many other things.
The main difference I see is that I'm aiming for a full adaptive system of information, including computation, not only note-taking (I bet you guys have more thoughts).Trying to figure this out has let me to quite deep rabbit-hole around language and semantics [1].
I've actually have a proof of concept running as my website [2], you can navigate about 500 of my "thoughts". Everything in there are transclusions, and the user-interface are notes/memos themselves.
I think we should talk :)
Hi, sorry I missed your reply. The email was indeed missing and it was added short after posting it here. You can just email me at xavi at vocdoni.io.
The documentation is a big beast and our source of truth, I'll highly appreciate if you can point me to the broken links.
It seems relevant to point out that there are two types of sweat glands [1]. And they secrete different stuff:
"Eccrine sweat is clear, odorless, and is composed of 98–99% water; it also contains NaCl, fatty acids, lactic acid, citric acid, ascorbic acid, urea, and uric acid. Its pH ranges from 4 to 6.8. On the other hand, the apocrine sweat has a pH of 6 to 7.5; it contains water, proteins, carbohydrate waste material, lipids, and steroids. The sweat is oily, cloudy, viscous, and originally odorless; it gains odor upon decomposition by bacteria. Because both apocrine glands and sebaceous glands open into the hair follicle, apocrine sweat is mixed with sebum."
The article mentions acid lactic as a signaling metric. Only the Eccrine glands sweat contains it.
This explains why the no-correlation between strong oddor (casused by the apocrine sweat).
I also want to point out that when running barefoot/minimal you reduce the stride and increase the cadence. In my experience the result of it is that speed its generally reduced, specially downhill and flat surface.
And by going completely barefoot the surface of the terrain it really defines the speed you can go. When going fast the pressure on the sole its greater and if the terrain its harsh you are forced to slow down. A lot of time until the point of walking, or even slower.
In complicated terrains the potential outcome for stepping over the wrong stone it really makes you to be conscious about every movement, slowing down as well.
I define both concepts fundamentally in relation to priors and possibilities:
- Entropy is the relationship between priors and ANY possibility, relative to the entire space of possibilities.
- Probability is the relationship between priors and a SPECIFIC possibility, relative to the entire space of possibilities.
The framing of priors and possibilities shows why entropy appears differently across disciplines like statistical mechanics and information theory. Entropy is not merely observer-dependent, but prior-dependent. Including priors not held by any specific observer but embedded in the framework itself. This helps resolve the apparent contradiction between objective and subjective interpretations of entropy.
It also defines possibilities as constraints imposed on an otherwise unrestricted reality. This framing unifies how possibility spaces are defined across frameworks.
[1]: https://buttondown.com/themeaninggap/archive/a-unified-persp...