Old Student

freeform, you seem to know Damo Mitchell's work fairly well. In White Moon on the Mountain Peak (p.158), and also in the article on Ding and Lu I cited above, he has a symbolic picture of them. It must come from Lu Daochun's Zhonghe ji (Compilation on the Middle Harmony), which is also from whence his term "firing process" comes. But this is the "An Lu", and this is the "Li Ding" in that book, and the trigrams above them are the reverse of Mitchell's. Any insight on why he switches them up?

I really meant give me a reference to the articles (perhaps by Hameroff and the Indian physicist in Japan) on which the following statement is based. As in what is the name of the articles. I found something for you that I think would help you understand the Fourier process and how it generalizes: Sorry for the embedding, I meant only to include the link. Pay careful attention to the way the picture is described by adding circles to the approximation.

Is that tugging in the same place where the mind is when the mind passes through the dantian, or is it perhaps elsewhere? Like elsewhere in the abdomen?

https://climatedataguide.ucar.edu/climate-data/total-solar-irradiance-tsi-datasets-overview Did you see the above link? If you can successfully show why that very periodic and not remarkable cycle is causing long term warming (long term being with respect to the time period of that TSI cycle data), then you can show that Hansen was wrong. But unless you're seeing something that isn't really there in that data, you can't. It just doesn't support any long term increases. That's what he was trying to tell you. You're dead set on trying to prove something other than human created emissions and human created changes to the environment are causing the increase in heat. He has the data that the heat isn't being created externally. He knows his stuff on that, he's a planetary climatologist. So if anyone is a zealot chasing a predetermined conclusion, it would seem to be the person who grabs any graph he can of other people's data without reading other people's explications of their data and tries to prove humans aren't doing this. We are. There are too many of us putting out too many wastes and tearing up too much nature. So like I said, I don't think I can do better explanations than Jim Hansen, he's kind of very good at explaining things to people. So if you didn't understand it when he said it, there's no hope I'm going to get through to you. I don't know how old you are, but odds are that Hansen was studying TSI cycles when you were in grade school. He knows them very cold. Tony Heller doesn't, he's a quack.

In terms of Fourier eigenfunctions (eigenfunctions of the Laplacian) no, not an analogy as long as you take any kind of vibration to be a "note". The theory doesn't have to be applied to a Laplacian or Dirac operator, in which case you can decide for yourself whether you want to call it music directly or an analogy to music. Personally, I have no problems with analogies and metaphors, they make up the basis of all language, and probably of all thought. Be aware that in some of what Connes is talking about, those notes are points, and in some they appear to be strings (as in string theory not as in musical strings, but they were named that by analogy to a real string vibrating). You also need to be aware that when a mathematician says a point in a space, or a point in a phase space, it can be pretty much anything at all, the collection of them plus some structure to the collection makes a space. I believe the precise statement is, "...is actually provided by a music theory." His statement is that taking the underlying point structure of his geometry to be chords, the laws of physics become a music theory, i.e. a theory of what chords to use when and where. Also please understand that there is a whole superstructure of spaces and groups and algebras and operators over each point in these mathematical spaces. Do you have a reference for the ultrasound and tubule stuff?

Yes, exactly! So the way the "ordinary" notes (the geometry that "commutes") is embedded in the two note frequencies is that for each (single) frequency there is a copy of the entire set of ordinary notes attached, making up all the two note frequencies that have it as a (let's say) 2nd note, and in fact there is one that is attached to silence (frequency of zero) is indeed one of them and represents all the single note entries in the two frequency bigger space. That's called a tensor product space and the noncommutative space is a space whose basis is the eigenfunctions created by the perturbation semi-group which is a subspace of that tensor product space, with the properties that they are all of unit size (same volume maybe?) and all self-adjoint (if the operators are compact as well, their eigenfunctions create a basis for the space, some operators can be proven the same even if they sometimes aren't well behaved). So it sets up to have a basis of the space of his two-note geometry.

Since we both are looking to understand this, I just found this on Damo Mitchell's Scholar Sage site, it is informative.

This is going to be hard. Okay, I have a challenge to focus on Ting and try to let my breath be. Thank you.

You directly? Like you asked him to explain it to you? And you appear not to have understood the explanation. Not worth my time if he couldn't do it.

I never said anything about a seesaw, that's the second time (first not here) someone has heard me say tipping point and thought I meant a seesaw. I distinctly remember describing it as a ridge between two basins that you tip over into one or the other. Yes there are "negative reinforcers" the problem is, we're blowing through them. And as you near the ridge at the basin boundary, the net effect of those reinforcers balances to zero, literally.

Would you like to tell people how? Clearing underbrush from millions of acres requires what kind of resources, and should the resources have come from CalFire? Seems to me they were fighting fires, which is now a year round occupation here mos t years. Furthermore, the fires started in fields, not in the forest. As for, That's just trash. The fires started because the winds were 80 knots. They downed power lines, just like they do in a nearly category 2 hurricane anywhere in the world. The fires also spread because the winds were 80 knots. That's enough wind energy to carry embers up to 2 miles. It's just junk to think that the fires spread on the ground when people could see the embers flying through the air. The fire started miles away from Paradise, it was in Paradise in 2 hours. Nothing travels that fast in forest floor brush. The fire moved so quickly in Paradise that a traffic jam caused by everybody trying to leave resulted in people being incinerated in their cars. We had no choice but to think about the fires 24/7 for weeks, we had canceled schools, closed businesses, a red sun at noon and air quality rated as dangerous to all. For those of us who do science or do health, we were focussed on this fire and what was causing it and what was happening the whole time. For somebody from back East to come walk through the forest with cameras rolling and falsely tell people that the problem was forest floor underbrush is just garbage. The only "politicizing the facts" that's going on is an online rewrite of what happened. What happened is that we were hit with an 80 mile an hour storm of 90+ degree air into brush and forests that hadn't seen a drop of rain since the Spring. Normally by that time there's one or more short showers that don't do a lot but ameliorate the dryness. That season, nada.

There are quite a few, it's kind of inherent in the concept of a tipping point. In dynamics, equilibria are basins in state space. Think of state space as create a dimension for every variable of the system. Then a point in the space represents a state. The path of a point represents the change or evolution of that state through time. When a system is in stable equilibrium, it is in a basin and on or moving towards an attractor, which is the equilibrium. The basin is due to the fact that if you move away from the equilibrium, since it is stable, you "roll" back down the basin surface to the attractor. A basin boundary is place where if you roll past it, you roll out of the basin, typically into a new one. So if you roll just up to the boundary, you roll back, if you pass it, you do not. Crossing that threshold changes what the new equilibrium is. If that equilibrium is, say, a much warmer planet, then once you pass into that basin, it won't matter what humans do anymore the climate will warm -- it will be what they call runaway warming. And basin boundaries are complicated. How complicated? Every pretty picture you've ever seen from the Mandlebrot set is a picture of the boundary of that set's basin at zero. So once passed, it isn't certain you can return. Some tipping points that will move us to much warmer climates are, e.g. the methane permafrost starts to melt, which means the CO2 equivalent in the atmosphere goes way up and keeps going up, and the climate warms pretty much until the fires start and the atmosphere permanently changes. That's an extreme one and one of your positive feedback loops. Others are more subtle. If an area goes from glaciated to unglaciated, the weather overhead changes -- part of that vortex effect I was talking about with the melting of the ice in the Arctic and the Tibetan Plateau. That doesn't come back when the climate cools to current levels because it takes an ice age to put that much ice down. And it will not just change the water supply for 3 billion people, it will permanently change the monsoons in the Indian ocean, which affect the entire planet.

I met the NASA Goddard team in 1984, we were at a fluids conference and our poster was next to theirs. I looked at their data, I looked at their math. You're going to have to do more to convince me that it was some kind of fraud. Corrections are corrections, mine is equally from first principles. Picking and choosing the physics you are going to believe isn't science.

One word of advice: Stay away from Tony Heller. He isn't an authority on the climate. California had two record fires last fall. Both burned more acreage than any fire in California history (the second surpassed the first). One of them set a record for the number of people killed. As for this season, as you and I have already agreed, we had a wet winter. That means that there have been less fires so far this calendar year. But don't get comfortable. It also means that there will be more grass and undergrowth. If we have another high brought on by a contraction in the Arctic Oscillation like last year, we will get another long dry season going all the way to November, and the high causes Diablo and Santa Ana winds that are hot, dry, and very high speed. Last year, the Diablo winds hit 80 mph, that's what caused the fires. Telling someone from California that we haven't had much in the way of forest fires isn't just climate denial. It contradicts experienced reality. Do you understand? There's no way I'm gonna believe Tony Heller instead of my lyin' eyes. Over and out.

Not really, it was an example of how a noncommutative geometry allowed the spectrum to completely define the geometry of the manifold. Not sure what to make of "renormalization has been wrong". Renormalization is a technique. No, I didn't claim that. The noncommutative geometry Connes creates is his perturbation semigroup of operators which is an extension of the "commutative" geometry, so there is a natural embedding of the latter into the former. The "commutative" geometry is within the noncommutative geometry, not the other way around. (followed by quote from professor) Seriously? A quantum physics professor said that? That sounds like Penrose's theory on quantum events accounting for the brain space problem. UMass would have been a better place to take quantum physics. Penrose's theory exists because there is a very real problem with current neuron theory -- it does not account for the storage capacity of the brain. So Penrose postulated that maybe some quantum phenomenon was accounting for the "computing" as a way to increase the computing power and account for the storage. It's an interesting theory, but I don't agree with it. There is far more possible "space" in the brain after one discards the notion that all the brain does is fire synapses in response to signals based on the synapse long term potentiation or long term depression. Still, it's strange that it would show up in a quantum physics class, other than in passing.

Again, like I told you, if you cannot understand the difference between the warmth of a summer and a warm event, or the warmth of a winter and a cold event, then you absolutely cannot understand climate science.

I'm referring to the massive pasting of stuff in exclamatory print without apparent science grounding. Over on another place in the forum, I'm being told that some of the neidan stuff requires patient cultivation of a foundation. Did you do that with your scientific understanding of the climate? I do look at the science. I posted that link to the PNAS special issue on tipping points, in response to, I think, voidisyinyang. Did any of you "look at the science" types read it? It provides a pretty comprehensive explanation of what to expect as each climate phenomenon changes, and changes for all intents and purposes permanently. T his past winter was wet. It was not cold. It was warm. I'm from California, so I would laugh at your suggestion that we are not getting droughts except that too many people have been killed already in fires so we don't think drought is a laughing matter here. The Arctic sea ice is contracting, and NASA has pictures of the contraction. It is not expanding.

Thanks for the correction. My turn to correct. It's simple physics, man. The Arctic Oscillation is complex, but largely its contractions and expansions are a result of the condition of the permafrost and monsoon cycles in Siberia and the underlying Arctic vortex is caused by the cold air sinking due to the ice in the polar ice cap. Cold air sinks. Sinking air is a high. Winds spin around a high. Got it? No cold air, no high, winds aren't as predictable. There are two other places where that happens on the earth, the Antarctic, and the Tibetan plateau, although that used to do that much more than it does today (say 11,000 years ago). I really need to ask, being kind of new to this site. Why all the climate denial? Is that a Daoist thing now?

Um, yes it does. Higher CO2 levels do produce warmer winters, the past winter was one of the warmest on record. Notwithstanding that there were any record cold temperatures measured. The warmth of the winter is an average, the record cold temperatures were events. And my point about El Nino is that during years when there is an El Nino, the Pacific Ocean is warmer, so it absorbs more CO2 which decreases the amount of increase in CO2 in the atmosphere temporarily. El Nino is a natural phenomenon (actually ocean not weather), but its timing and intensity and cycle are affected by global warming. We have not had record cold winters, we've set cold records in winters. There's a difference. If you cannot understand that difference, then forget talking about the climate, which is usually studied on a decadal or even millennial timespan. The difference between a cold winter and a winter during which there were record colds, is that a cold winter is cold over the timespan of the whole winter, and we haven't had any of those lately, the past winter was IRRC third warmest on record. What we have had is some records set for cold, i.e. days when the temperature was colder than for that day any time on record. That's due to the instabilities in the winds that circle around the Arctic, which cause what is reported in the weather as polar vortex. And the fact that that happens more frequently than it used to is due to the warming of the Arctic -- i.e. due to loss of permanent Arctic ice. This stuff is done by science, not by shouting. Warm an ocean, gases dissolve better, cool an Arctic, produce winds corresponding to the permanent downdraft because cold air sinks. NASA has a great video of Rossby waves if you want to see how the Arctic causes weather. And this site is a continuously running blog on the Arctic Oscillation. Read up if you want to know more about how weather and climate interact.

It's the mind used for pushing hands. But it usually makes my breath die away. No, for me, standing is easier than sitting, if the time period exceeds 1/2 hour.

So the analysis is that you choose a group of operators, then you create what Connes calls it's perturbation semi-group, by taking its tensor product with itself with his operations for creating the semi-group, which involve operations of multiplication using the resolvent of another operator previously specified, and moving to a subset of that product that fits his normalization and adjoint conditions. Spec. if f(x,y) is an operator in the tensor product, we require f(x,x)=I the identity matrix, and f(x,y) = conjugate transpose = f(y,x) conjugate. On the new set, you get extra structure, and the specific operators he's interested in are the eigenfunctions of the Laplacian, and the eigenfunctions of the Dirac operator, it's formal square root. What it has to do directly with music has to do with Milnor's theorem that the spectrum of the Laplacian does not in general determine the shape of a manifold (in this case think surface with boundary), answering Mark Kac's query in his Math Monthly article in the negative (presumably that was what Kac was writing about.) If that's the case, then in the specific case of a drum, where the eigenfunctions are the waves across the drum head that resonate, this means that you can't necessarily tell what shape the drum head is by listening to it always (you famously can tell a square one from a round one because a round one can be tuned -- like a tympani and a square one doesn't have a "tone"). As for whether you are talking block diagonal or diagonal matrices, nothing prevents using block diagonal matrices, what I was telling you was what the eigenvalues of a matrix are, and it is a fact (called the Jordan canonical form) that all matrices with non-zero determinant can be diagonalized over the complex numbers -- at which point the diagonal entries are the eigenvalues. The paper you pointed to does indeed say that the normal geometry embeds (i.e. the original Laplacian and its eigenfunctions are part of the noncommutative structure constructed from them). It embeds because it is tensored with itself to give the space from which the perturbation semigroup is constructed. One can construct a Dirac operator on any space for which the Laplacian for that space has been constructed. Constructing such a Laplacian, IRRC, requires that the space be a symmetric space. On such spaces, the Laplacian has eigenfunctions which function as the Fourier series components for the space. What I was telling you is that those spaces need not look at all like the spaces in which you are familiar with the Fourier components and in which they represent frequencies. You could still call them frequencies, but, for instance, the frequencies you make your music from are related to the Laplacian on a 2-sphere (sine and cosine waves), and what they are on an infinite dimensional sphere is probably a bit different. And some of the exponents, for instance, in the paper you were reading on music, you know, eD where D is an operator, are different, they are defined in terms of infinite series and in the non-commutative (usual) case, the exponents don't add like they do when they are numbers. So it all looks like it's the same finite mundane world of functions and addition and multiplication and stuff, but it's frequently infinite dimensional and not quite the same. I tried not to use to much jargon, and this isn't a place to write formulas (there's no MathJax), but I hope this helps.

You do know we have an El Nino this winter/spring? It causes rain in the U.S. West over the Sierras and Rockies. Elsewhere in the world except for Southeastern Africa, it causes drought. Also, there is a balance: CO2 dissolves better in warmer water than colder, so CO2 increases measured in the atmosphere should slow down during El Nino years. As for "coldest winters" in the U.S., haven't had any recently. We've had record lows, caused, as you say, by wobbles in the Arctic winds which shed into our airspace. But those are actually caused by the melting in the Arctic which destabilizes those winds. When the ice is thick up there, those circumferential winds are very stable, and we don't get polar vortex as much.

No, that wasn't really quoting what I said because I meant, and said, "discrete and continuous". Spectra of (closed) operators on a Hilbert space have 3 parts: The resolvent, the discrete spectrum, and the continuous spectrum. So I really did mean "discrete and continous" as in a spectrum that includes both. In particular, if you have a self-adjoint operator, it's spectrum is real, and if it is not commutative, the commutation operator gives an uncertainty like the Heisenberg uncertainty principle. These spectra don't have to have anything to do with frequencies, it is when they are Fourier spectra that they correspond to such, which is where the name came from -- why they are called spectra. In this case, they are the eigenfunctions of the operator, and the best analogy is to the eigenvalues of a matrix (If a matrix has determinant not zero, you can find a coordinate system in which it is a diagonal matrix and the eigenvalues are the elements on the diagonal). Good to know, I do find your stuff inspiring for mental images. My background, with respect to this stuff is mathematics, spec. dynamical systems and chaos, and I have undergrad and a little grad physics. I suppose that's true, but not what I meant. I have an erstwhile professional now retired interest in some differential geometry topics, the Ricci equation and anisotropic diffusion. There's some overlap with Connes' subject matter, but only some. I do sometimes read stuff about string theory, but not in any mathematical depth. And I do have my own use for discretization in my topic, which is why I thanked you for the references. It actually refers to the spectrum of the Dirac operator. The Dirac operator is the formal square root of the Laplace-Beltrami operator (so that actually is something I get to use from time to time). But like I said, because some operators have spectra that are related to frequency, they are all called spectra as an analogy to light spectra. That one, because it's related to the Laplace operator, whose spectrum is Fourier eigenfunctions which really are frequencies as in frequency domain, is easier to picture as frequencies than most operators in general. Connes' point in relating everything to music is to try to make everyone intuit the notion of noncommutative geometry as easily as they can intuit other geometries. Because he wants to end the dichotomous thinking about classical v. quantum physics and think of the whole as one physics.

It does help, thank you. I'm very familiar with the posture, and can relax into it and fa sung. So I guess it's to learn to sink my mind, which this: is very instructive. By not focusing or directing, I'm assuming I'm using to much yi 意? My usual way of "turning that off" is to remind myself when I start using it that, "I don't know how to do this, I need to stop knowing how to do this," before relaxing my thoughts. I will try this. Thank you, and thank you for the dantian position behind the qihai.

Thanks for the lecture quote. Question: Did you insert the bracketed words -- "[frequency]" next to the word "spectrum"? Alain Connes seems to be talking about the spectra of operators, not of waves. Because such spectra are capable of being discrete and continuous. I was taking that from the following (Connes, A. Noncommutative geometry and reality. J. Math Phys, 34(3) 1995, pp. 6194-6231.): I haven't read the paper, it isn't what I'm working on right now, and would require a lot of digging for me. But it doesn't appear to displace or call untrue the use of Riemannian geometry where the length scales are appropriate, it includes Riemannian geometry (if I had to guess, not having read more than the intro, Riemannian geometry emerges as the model for the continuous part of the spectra of non-commuting operators).