joigus

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.

Yeah I knew Ne'eman was related to the higher echelons of Israeli politics, or the military. I do remember an interview with Gell-Mann in which he mentioned Y. Ne'eman's interests really lay in general relativity, but he was somehow forced into particle physics. I do consider this era of physics kind of a heroic one. It's not for everybody to find your bearings in this terrain of approximate symmetries and mass formulas, empirically guessed relations and the like. Great respect on my part.

You have to distinguish total spin J=3/2 from spin projection. A particle of total spin J has 2J+1 possible spin projections. Eg, a particle of spin 1/2 has 2*(1/2)+1=2 spin projections, which are -1/2, +1/2. In the case of omegas, we have 2*3/2+1=4 possible spin projections, which are -3/2, -1/2, +1/2, and +3/2. If omegas lasted long enough, we would be able to perfom a Stern-Gerlach experiment and separate them into 4 distinct beams, I'm sure. Omega- has spin 3/2 for the reason that these are isospin multiplets, so all the particles in the n-plet have the same spin. The ultimate reason for that is the concept of approximate symmetry iso-spin='same spin'. IOW, baryons with the same spin have approximately the same mass. Exactly. I wouldn't call it S, as that's reserved for strangeness. I particle physics it's traditionally called J.

Elementary algebra, as others said or implied, is using the properties of numbers that are known to be satisfied for every number in order to, eg, solve equations among other things. The word comes from an old Arabic term, al jabr, which means something like 'the restoration'. There is a so-called abstract algebra, in which you generalise the idea to less familiar, but quite consistent, quantities and operations: rings, groups, and so on. I hope that helps / complements what other have --correctly-- said.

Yes, I forgot that. I've mentioned it elsewhere in these forums though I think, or I should have, when talking about language. Brain studies indicate that the areas of the brain that usually code for sounds are used to code for images --sequences of images[?]-- in the case of people with this particular disability. I'm sorry I don't have the biblio with me. It's covered in Stanford lectures on human behaviour by Sapolsky. Makes you think whether the most primitive languages really were a mixture of mime and sounds.

I č ne cnēƿ sē According to my dictionary at hand, I've answered you in English, only Old English. If English was evolving in the seventh century, I see no reason to assume it's not doing so right now. What's probably true is that the path and the patterns, and the speed of change, are different, as communities today interact in very different ways than they used to do back then. Of course languages evolve. Centuries upon centuries of 'contamination' are perceived as 'evolution' when a sufficient number of people perceived as educated adopt those ways of expression, and refine them to remove ambiguity and add nuances. Language is very plastic. There is no such thing as the right way to say things. I'm no expert, so don't take anything I say on authority, of course. But I've interacted with experts enough to know that something like this is what's known to be the ongoing process of language evolution. Agreed. Language is a two-pronged process, I would say. Writing is, after all, a sophistication, and an priceless tool, but it's derived from speaking. Language stems from a phonetic code. Speaking is no doubt much older than writing. Grammar is an afterthought. In our heart of hearts we know there is an implicit order and hierarchy, and we try to clarify it by spelling out some rules. But the process itself is much more spontaneous.

Are you familiar with the concept of subpar? --American English.

So you claim to understand what isolation in time and interacting time mean? Care to explain it to everybody else?

Another postmodernist outcry.

This is the simplest and thereby most beautiful way to explain the argument, IMO. It's the version I was exposed to. After reading most of the material here I'm convinced it's not the way in which Cantor formulated it historically. Probably. I don't know the history of it. I don't read German either, but I doubt any ambiguities might be lurking behind a more or less obscure German word. I agree that modern formulations tend to streamline the proofs in a very interesting way. I like your phrasing: Any list of numbers that purports to be listing a connected piece of the continuum of real numbers must necessarily be missing a string. The diagonal operation of somebody's version of Cantor's theorem goes on to prove in a glaringly obvious way, that we can always construct a number not in the declared list. The truth of such declaration is thus impossible. I'm at a loss as to what else is there to be unravelled in such a simple argument.

Is that spontaneous symmetry breaking?

Some questions: How can a single proton or neutron have a meaningful entropy? What kind of entropy is that? What do the terms "time interacts" or "isolated in time" mean? BTW, photons have no mass.