joigus

Sure it is. In fact, given enough context, a complete reference to the terms could become unnecessary, and saying 'I see' or 'I don't think so' could be enough to make clear what one means. If you think about it, we use elipsis most of the time when we are with family or close friends. They know what we mean. When I said syntax must have been present very early on, I meant that even in the first stages of development of language there must have been a very simple set of rules (subject)+(action)+(object) --or inverse order--, (subject)+(be)+(attribute). I don't think that crude pointing at things and naming could have been going on for much long. Linguists call this proto-syntax. It is, no doubt, speculation on the part of linguists --as language leaves no fossils--, but a very reasonable one. So obviously all words are more words couldn't be farther off the mark.

Or said index finger, but only when it's pointing to a rock. I think syntax is necessary very early on.

You would think so, but once a symbol has been introduced, it seems to acquire a 'combinatorial' life of its own, so to speak, that would make it very difficult for anyone to try to guess the meaning from just watching the symbol. In this respect, I found this talk by David Perlmutter very interesting: It seems to suggest that this direct association between meaning and symbol is but an initial cue, and complicating factors come into play later. Particularly interesting are his comments on how nearly indistinguishable the two symbols for 'Canada' and 'Jom Kippur' are in ISL.

De Saussure already observed that symbols are arbitrary --except probably for onomatopoeia--, while associations of symbols are not. OP seems to be confusing 'arbitrary' with 'silly', and not taking the second step --associations-- at all. Let's see what they have to say for themselves.

Very interesting. Here's a cute YT video on the 'mechanical' version of it, (https://en.wikipedia.org/wiki/Braess's_paradox#Springs) Sorry that it's a bit off-topic.

Very good example of,

I'd say that your feel of how slowly something grows largely depends on how often and how intently you observe it. Remember that saying, 'it's like watching grass grow'?

Interesting...

I think what @Genady means is space is not some "stuff" of which you can put in more of it. I agree with pretty much everything else he --and others-- have said here. You can't use naive addition of velocities to "cancel out" receding speed of galaxies with speed of light. Both have dimensions of length / time, but are very different things. One is an expansion parameter that applies to the whole of the universe as per cosmological standard model; the other is the speed of photons when they go "past your nose" so to speak. The latter is always c (a universal constant.) For photons reaching you from near the cosmic horizon, what you get is extreme Doppler shift, so they are lower and lower frequency (longer and longer wavelenght) the closer you get to this horizon. This horizon is of a kinematical nature, but it doesn't manifest itself as stopping the photons in their tracks, but as making them closer and closer to invisible. The other mistake that you're making --ignoring space expansion since those photons were emitted-- I also agree with. The fact that it's a mistake, that is.

Things obviously have changed a bit since 1977, but it's always nice to listen to Feynman afresh. This talk was unknown to me, and I still haven't got around to it, but Feynman never disappoints. Enjoy.

This calculation seems to be correct. Just in case anybody's interested, and because this thread has recently been revived, there's another definition that overlaps with that of a factorial (or gamma function). Namely, the falling and rising factorials. Although it's a generalisation in a different sense. The variable is not the "n" in n!

I thought this might be a meaty topic of discussion --based on the title--, instead I find what looks very much like a hall of fame of people with receding hairline through history.

I bet on lazy journalism. I recently read "prices of groceries going down" as synonymous of "inflation of groceries going down". Then corrected in 24 hours in follow-ups of same topic.

Agreed. Not a language issue to me. Just plain wrong. Dear @Z.10.46, there is a game in town that's very similar to what you're trying to play here. It's called asymptotics. From: https://en.wikipedia.org/wiki/Asymptotic_analysis In asymptotics we have to be very careful though. We never use the = sign. But we use an equivalence relation \( \approx \). If, eg, \( x \) is "very small", you're allowed to do things like \( \left( 1+x \right)^{2} \approx 1+2x \), but never things like \( x \approx 0 \), which lead to sorry mistakes. There is no such thing as "infinity" in asymptotics; only very big quantities, which must be either possitive or negative. Otherwise --like in your quite absurd, dimensionally inconsistent expression--, the "quantity" \( x \) defined by \( x + 2 = 1/(c-v) \) with c=v is: 1) +infinity? That is, the right limit, or, 2) -infinity? That is, the left limit. Of course infinity +2 = infinity, but also infinity + 3 = infinity, infinity +17=infinity-1/pi, etc. And -infinity+2 = -infinity, etc. "Infinity" is not a number. It breaks all the algebraic rules. Example infinity + x = infinity + y does not imply x=y. I like to think of infinity more like a topological entity (the boundary of the real numbers). I think that's the way in which modern mathematics we tend to look upon it. But that's another story. And Swansont's objection about units still stands.

My Dunning-Kruger effect sensor went off the scale here. Your handling of units and zero/infinity is appaling.

Also, you got this wrong --perhaps a typo. The famous regularisation of this infinite divergent sum by means of the eta function produces -1/12.

That's not what regularisation/renormalisation is about. And there is zero in physics, as they've repeatedly told you. The charge of the neutron is zero, for example. It's not a tiny little non-zero smidgen of a thing. It's zero.

You will have to be more specific.

Are you trying to frame me? On a side note: I was just trying to be poetic in the face of frustration.

I think you make some good points. Mathematicians have developed tools like fuzzy logic and the like that maybe could some day applied to the natural sciences successfully --meaning usefully. The thing about "seeing the wood from the trees" is that I don't know how you do that when what we're talking about is the whole physical universe. I'm not sure that there's a valid outlook that allows you to say, "oh, I see, it's just a wood!" I love that sentence by Carl Sagan --above any other quote by him--, which says, which is the very beginning of his series Cosmos.

I'm having problems with "contiguous with all of itself". Do you mean something like all the information about the universe stored in the last least bit of it? There is a proposed principle that's called the holographic principle, that all the information about a region of the universe is stored in the surface. Reminds me a bit of what you're saying, but I'm not sure.

This 'when the ties are broken' that you're articulating here is very much like what I was trying to suggest when I talked about the denial of the unseparable whole being so useful. Some situations, like entanglement, or Fermi gases/Bose condensates etc (QM) remind us of how this separability falls apart quite naturally in certain contexts. In a context like here and now --the Earth 2.7 billion years after its formation--, we tend to see the world as interacting parts. When the universe was but a fraction of a second old and in a state of plasma, it's very difficult to conceive of an entity being able to distinguish anything like parts interacting. Analysis is best defined as studying something in terms of its constituent parts. The Greek lysis root gives it away. Lysis = breaking up. A big part of the method of science is analysis. I don't know how else to do science. Trying to describe the whole --whatever that means-- by means of analysis would --so it seems-- necessarily defeat the purpose, wouldn't it?

Of course everything is one whole. The problem is what to do with that. And what's more, why is the denial of this monumental truism so useful?

It's always going to be ambiguous. You need sedimentary deposits in order to have a clear-cut boundary that tells you when things really started to really go this or that way on a global level. You have to give geology some time.