joigus

I don't think you deserve that title. "Watchful eye" is more like it. And there's certainly nothing wrong with that.

If you allow me a to maintain my analogy a little longer; if the tumor is not malignant, it may just result in giving you an awesome tattoo that distinguishes you from the boring un-tattooed atheists. You are not enslaved and you keep your cool religious gear. What's not to like? I don't see mindfulness or the like as a variation; rather, as a much healthier substitute. But that's just how I view it.

I see, you're right. Thank you, @swansont. +1 To tell you the truth, I was thinking about possible atmospheric drags to make an edit of self-corrections, but I missed the perturbative factors if you want to keep the orbit periodic, which should have been pretty obvious to me.

No thrust at all. Just inertia.

There's one fundamental difference, though. Dynamical trajectories can't cross paths.

I think religion is very much like a skin tumor. It's there for a reason different entirely from what humans need or wish. You get it or not more or less likely depending on your exposure to "the light" as much as on how strong your defense system is, and it can become just a quirk or turn into melanoma. But, as any other self-maintaining, replicating process in Nature, it couldn't care less about what you really want or need. It grows because it can. If you're lucky enough to weed it out, you can concentrate on the much more interesting problem of where it comes from and why it sticks in so many minds (some of them, curiously enough, anything but stupid,) or why it took the form it did in the particular part of the world where you were raised. Why the Bible took the form it did, I think can be understood largely in terms of history and archaeology.

Aaah, yes. I had forgotten that one. +1

We have the same religion. +1.

Although I've been out of touch with programming for a while, I do remember lots of confusion with languages as "cavalier" as PERL, for example. 😮 I don't know how to answer to your interesting "side note/speculation/question"!!! Thank you. Very interesting addition to the initial question. I personally have never found @MigL at fault in rigour. 😲

Not to be a nitpicker, but the main point of chaos theory is about mixing of trajectories, not so much instability, although instability (high sensitivity to initial conditions is a better term) is defined as a necessary condition. So two trajectories might separate from each other for some time in a chaotic system, but then get closer again, and then grow apart again, so as to "almost densely" cover all the phase space. While it is true that it's a matter of definition, look at the revealing fact that the word "mixing" appears 13 times in the Wikipedia article, while the word "unstable" appears only twice and the word "instability", just once in a reference. Certainly instability is a necessary condition for what's called chaos in dynamical systems to appear. Look at what the chaotic dynamics of a system does to a cluster of point in the phase space only after six steps of iteration: Chaotic trajectories look very much like what a child would do when trying to fill in a piece of paper by drawing a line squiggling all around the place.

Actually, @MigL, I think that an excessive attention to precision can be as much crippling as a lack of it. The reason of my post is that I've seen people going around in circles because of their inability to understand that they're using a definition, instead of an equation. That's the opposite end of the spectrum. TBH, I don't think all the distinctions I've made are all that important. But being able to tell a definition from an equation really is a major mistake, that I don't think you, for example, would ever make.

No quarrel with this.

Wrong forum, perhaps? 🤣

Oh, yes, "estar por" ("estoy por creerte") "dar por" ("le dieron por muerto") "tener por" ("lo tengo por cierto") "deber" = must "deber de" = might "pasarse sin" ("puedo pasarme sin ello") LOL. Probably hundreds of those more. I think we tend to oversimplify other people's language. Most of the rules are learnt by use, not by reading lists or studying grammar and syntax. Nice contribs. @studiot & @vexspits (+1,+1) Thanks a lot. Edit: Sorry, you already mentioned this one.

Some of the latest posts in Speculations have led me to this attempt at clarification, because I see that some people are very confused when it comes to handling equalities. The point is their meaning. It's subtle, but it's not moot in general; although in some cases it may be. Not all equalities are the same. There are at least these variants: Definition (or substituting symbol or replacing symbol, etc.) Example: fine structure constant, \[\alpha\overset{{\scriptstyle \textrm{def}}}{=}\frac{e^{2}}{4\pi\epsilon_{0}\hbar c}\] Identity (or universal equivalence under known or specified set of previous rules that may be algebraic, geometric, etc.) Example: constriction between sine and cosine, \[\sin^{2}\theta+\cos^{2}\theta\equiv1\] Equation (proposed equivalence considered in relation to the finding of "solvers" or "solutions") Example: Pythagorean Theorem assumed true, solve for c2, given c1 and h, \[5^{2}=\left(c_{1}\right)^{2}+3^{2}\] Formula (proposed equivalence under non-universal, somehow hidden, or not necessarily specified assumptions) Example: Pythagorean Theorem, \[h^{2}\overset{\cdot}{=}\left(c_{1}\right)^{2}+\left(c_{2}\right)^{2}\] Some formulas can become equations once you give values to terms or supply additional information. And yes, sometimes the distinction between what is a formula and what an identity can be blurry, depending on how we look at the defining "valid rules." E.g., the constriction between sine and cosine can be seen as an identity if we take Euler's identities, \[\sin\theta\equiv\frac{e^{i\theta}-e^{-i\theta}}{2i}\] \[\cos\theta\equiv\frac{e^{i\theta}+e^{-i\theta}}{2}\] as the point of departure; or a formula, if we adopt Pythagoras' theorem plus geometrical definitions of sine and cosine. It may also depend on assumptions about curvature of space, etc. Needless to say, most people who use mathematics on a regular basis, don't need to be reminded of these distinctions, because they intuitively know what they're about. The danger is when people start playing with equalities (especially definitions, as I've seen) thinking they have a different value than they really do. Also needless to say, but better said, the symbols for eq., id., form., and def. are not intended for general use, but just to illustrate how confusing all this proves to be to many people.

Very good summary. And very good point. +1

Where can you see the error, please? The article is quite long... Yes, my favourite example are phrasals. The verb "look" is my preferred example: look into look after look down on look up to ... Completely different meanings. In Spanish those are fused: "comprender", "aprender", "desprender", "reprender", "sorprender"

Maybe an interesting book (I haven't read but I've heard about) in that regard could be Misquoting Jesus. When you take a religion to a different geographical region there are bound to be changes. That's what happened to Christianism: Sabbath --> Sunday (Apollo's cult by Constantine required that change;) drop circumcision and kosher, etc. I'm sure the Zoroastrians who wrote the Vedas were forced to similar changes when they passed from places like Kazakhstan to northern India.

Nice link. +1. One of the first imprints of sea animals strolling (or maybe hurrying) ashore is in so-called* Track Central, Kalbarri National Park, Australia. Silurian sea scorpions of the genus Eurypterid seemed to follow in the footsteps of other arthropods, Kalbarria. http://www.dmp.wa.gov.au/Trace-fossils-of-the-Tumblagooda-1667.aspx It's by no means sure that Kalbarria were the first animals, but those are the first traces I know of. Wonderful PBS documentary Australia's First Four Billion Years. * Non-official name, AFAIK.

+1. Very interesting. I find it amusing that in German spoons are boys, forks are girls, and knives are hermaphrodites.

Interesting. +1 Does Yanchilin's theory predict deviations from GR?

I don't know. It's been a while since I studied French. But what you say is definitely what I would expect.

There seems to be an insurmountable time gap with either John the Baptist or Jesus as possibilities. Lawrence Shiffman has argued very eloquently against that hypothesis IMO. His arguments rest on archaic Hebrew calligraphy, rather than 14C. He's convinced me, anyway, that it couldn't possibly have been anybody during the Roman invasion, but someone pre-dating that, during a Greek invasion scenario. Which makes it even more interesting along the lines that you're suggesting, because it would mean that religious leaders of small flocks fleeing Jerusalem's central authority and establishing a new brand of Judaism in the desert already was a relatively common phenomenon 100 years before. As you said: Leaders for time of hardship. This line of inquiry resonates with me, at least, because I think it's far more important to understand the appearance of religions based on the culture and the historical background than actually give a name or a biography, or finding the missing piece of the cross.

That's some rubbernecking for me to do.

That's one of the most fascinating features of English, which is, of course, a life-long project for me to understand. Another observation is: In English you have a sort of a nucleated but de-centralised structure of different authorities of several degree. Oxford prescriptions, Merriam-Webster prescriptions, etc. Quite different from Spanish, for example. That's at least my intuition of how it works and organizes itself, and interfaces. Maybe just coincidental, but this strongly parallels how the Protestant and the Catholic worlds have organised themselves throughout history. The Protestant, more multi-branched; the Catholic, more unified around a leader. It's only very recently that Spanish academies have clustered, so to speak, in a similar way.