joigus

Mmmm. Suggestion: Let it grow a little bit more and take another picture.

Thanks. And you're dead right. +1. I stepped back on this particular topic because Swansont and you were more focused and had this more under control and I wasn't helping. I was "waxing theoretical". I think that's the idea.

It definitely looks like some kind of marasmius. Only Marasmius oreades is edible, and fleshier, of those I know. Most of them generally look very much like the one you got there. A good representative is Marasmius capillaris: https://www.google.com/search?tbm=isch&sxsrf=ALeKk03N8VOMmcPUcPsa5XQgDzLvbwg5Ag%3A1595675562082&source=hp&biw=1280&bih=856&ei=qhMcX_7LAsW6aZH9qNAL&q=marasmius+capillaris&oq=marasmius+capillaris&gs_lcp=CgNpbWcQAzICCAA6BAgjECc6BQgAELEDOgQIABAeOgYIABAIEB5QmAFYvSpgkyxoAXAAeAGAAbMCiAH_EpIBCDE0LjQuMi4xmAEAoAEBqgELZ3dzLXdpei1pbWc&sclient=img&ved=0ahUKEwj-yLXYoujqAhVFXRoKHZE-CroQ4dUDCAY&uact=5 Most of them also grow on dead leaves. I'd forgotten most of what I used to know about fungi. I had to look it up and bring back memories. Thank you for bringing this up. +1

Apparently you see some need for calming down. I'm personally at my calmest. It would be nice if you quoted me with some actual content.

Yes! It's only that there were several lemmas. Wick's theorem was the re-ordering trick; and then you sandwiched the operators with the vacuum and got the ready-to-use result, which maybe had another name, an acronym like FDW or something... But Wick is one of the central names in the bunch of results. I'll go back to your other arguments later. You make very good points. We have similar line of thinking about one particular central question (space-time as shaped by conscience rather than fundamental). But you see an obstacle that I don't, so I'm interested. If you see an obstacle (or maybe a leap of faith or gap) it's definitely worth considering. Another post led me into thinking about the nature of space itself, so there's food for thought there too. I posted a comment that was very naive. I had to correct myself. Measuring space is not as straightforward as I thought when I applied SR's definition based on light rays going back and forth. What about very distant objects? You must appeal to indirect methods to guess the age of stars. So, nothing simple or straightforward about that from a practical POV... Anyway. Later.

Very similar arguments (the fact that you can add an arbitrary 4-momentum to a physical 4-momentum without changing its on-shell character) appears in theorems in QFT like, Soft boson theorems (soft pion theorems first historical argument) Ward-Takahashi identities Definition of Feynman's propagator: integral extended to all momenta, including off-shell: https://en.wikipedia.org/wiki/Propagator#Scalar_propagator Take a look at this scalar propagator. It's an integral to the whole momentum space. Edit: More info for you, @studiot. Off-shell amplitudes in the propagator have to do with internal legs in Feynman diagrams. The amplitude for a particle to be created at one point and annihilated at another. The soft-boson idea is to do with low-energy (virtual) bosons that escape to infinity (external legs in Feynman diagrams). Another bundle of key words for it is "infrared divergences". When you calculate the cross section in, e.g., QED, even after you renormalise charge, mass, etc., it still has infinities due to arbitrarily low-energy ("soft") photons going off in all directions. You must do a cut off to remove those photons you will never detect on account of your detectors having an effective energy threshold (they can't detect arbitrarily "soft" photons escaping to infinity).

Wrong method?

Yes, I think you're right that depletion is not that important. I was so stumped by the humongously big number that I didn't know what to think. You could try to work it out with the barometric density formula: https://en.wikipedia.org/wiki/Barometric_formula#:~:text=The barometric formula%2C sometimes called,1000 meters above sea level. Both expressions, for pressure and density, are basically the same, \[\rho\left(r\right)=\rho_{0}e^{-V\left(r\right)/k_{B}T\left(r\right)}\] But they are isothermal expressions. The leap of faith I've tried is assuming that you can substitute T by T(r). I'm not sure that would hold. You could always take a look at the wiki derivation and try to work it out for little slices of width dr and constant temperature for each slice. My sub_zero is value at the surface. Maybe that's the ticket.

Not a very useful line of thinking for homework help.

My hippocampus doesn't quite agree with that.

It depends.

Why do you want to augment your brain (or anybody else's)? Why not improve synapse, efficiency of multiplexing, neuron plasticity or ability to regenerate? Brains are not breasts.

Not even wrong.

How do you know consciousness is continuous? What does "continuous" mean? "Continuous" is a sophisticated mathematical concept. A topological set is continuous if it contains its closure. What's the topology? Edit: Sorry. Closed, not continuous. But it's the same really in this context. A continuum must be closed.

Are you suggesting beta decay is playing a role in conscience?

The very fact that you talk about quantum coherence in a mesh of organic tissue at near 310 K proves to me that you are clueless about the meaning of the concept. The fact that you've mentioned gravity in a context where polar electrostatic forces are orders of magnitude bigger proves to me that you are clueless about constants of Nature and dimensional scales. You don't make sense philosophically either: Your room is not you. Your notepad is not your ideas, etc.

No knowing agent has to know anything. Embryonic stem cells make brains, and livers, and lungs, without anybody conscious orchestrating it. It seems to be the current informed opinion that quantum coherence plays no role in brains, human or otherwise. It could be. But it's not likely, to say the least. Quantum coherence cannot be preserved in such a system as a brain. The electron positions are irrelevant for all we know. I'm not aware of any serious model that contemplates quantum mechanics and gravitation as playing a fundamental role in conscience either. You're using a very loose logic. Something like: quantum mechanics and gravity imply entropy, which implies information, which implies brains and conscience. That's not how it works. That much can be said even not knowing how it really works.

I agree that pressure must go up as you go down towards the centre of the Earth. I also agree that temperature is important and must go up (however gradually) as you go down. Up to about 6000 Celsius at the centre. I've made a quick check with the following model: 1) the amount of air within the shaft does not deplete the atmosphere significantly 2) Gravitational field is obtained inside the Earth by applying Gauss's theorem 3) Exponential atmosphere is assumed with T as a function of r (distance from centre of Earth) and V(r) the expression for the interior potential \[P\left(r\right)=P_{0}e^{-V\left(r\right)/k_{B}T\left(r\right)}\] The expression for the interior potential is, \[V_{\textrm{int}}\left(r\right)=G\frac{M_{\oplus}}{2R_{\oplus}}\left[\left(\frac{r}{R_{\oplus}}\right)^{2}-3\right]\] And the model doesn't seem to work. It gives a ridiculously high value for the pressure; much, much bigger than 3.8 trillion psi, which is the value for the centre of the Sun! 😲 To me, this means that at least one of hypotheses 1), 2) or 3) is plain wrong. The most suspect to me is 1). Maybe what would happen is that the whole atmosphere would be swallowed up by the shaft density deficit, and it would cram itself into it, thereby depleting the outer atmosphere. Assumption 1) is implicit in that P0 keeps its current value, even though the whole atmosphere would have been sucked into the shaft. P0 is the 14 psi reference value that @Janus has mentioned. A more realistic model should involve the distinction between crust and mantle (discontinuous layers). But I don't think that would make that much of a difference. Maybe I made a mistake or the simple substitution in exponential atmosphere relation with the temperature as a function of r simply does not hold. Why do you see the density-pressure dependence as a problem, @Martoonsky? What particular model are you trying to apply?

Interesting question, but too loosely defined, as @iNow points out. One very important thing you must clarify in my opinion is whether you are considering developmental biology. You can't just practice surgery, or implants technology in order to do that. Brains develop slowly, and the growth process monitored by enzymes, I surmise, is very important in the forming of such a complex organ as the brain.

I would just add "degrees of certainty" to your list, which I just assume you've thought about before. How you grade concepts in a meaningful and useful way is another matter, of course. I'm trying to get closer to precisely this concept you mention. Namely: What would be a good criterion for a "philosophy of science"?

Why do you mention spherical coordinates in relation to time? Have you got something in mind? I've got something in mind, but you go first.

This connection is fleshed out by a theorem (I forget the name now) that relates time-ordering of operators with expected values in the vacuum for normal-ordered products. Irrespective of technicalities, this strongly suggests that time in getting in the way because of its being very very deeply entrenched in our language, or sequential alphabet, or what have you. I hope it's clear what I mean, although I recognize that what I mean is difficult to make explicit in terms of language and symbols.

A must-read for this post. +1

True. +1

Well, I was going for minimal conditions for a time to be possible to define (from a purely mathematical POV, so no operationalism, no clocks at this stage). Another example to add to the ones you provide in which this technique wouldn't quite work are chaotic systems, because for chaotic systems there aren't nearly enough integrals of motion to reduce the dynamics to a clear trajectory that can be pictured as an implicit relation between your dynamical variables of which a one-parameter could be deduced. To me, once you have defined (in clear-enough cases) this one parameter that suggests to you a sequencing of events, you still have the enormous freedom to choose which particular parametrization corresponds to your clocks, how different sets of clocks relate to one another, etc. That would be problematic if one photon were the only thing that exists in the universe (you could always define an affine parametrization for a photon which is what people do to describe the geodesic equation for photons, but the interpretation of such parameter as a time is another matter). In the scenario that I'm talking about, there are more things, and the coordinates of the photon could in principle be included in the aforementioned implicit equations fi(xmatter,pmatter,xphoton,kphoton)=0, so a one-parameter sequencing for the whole system would be possible to define. Now, on the proviso that this sequencing can serve as the minimal condition for a time to be definable, and taking into consideration your caveats about clocks (the question would be pending of what re-parametrization of this emergent parameter to use so that it corresponds to our physical clocks), there's still the subtle matter that it's defined from a metric or pseudo-metric. And these are always based in physics on quadratic forms, and thereby you must chose an orientation for the sequencing parameter to run along. Here I think you took me a little bit too seriously. Mind you, I said: So I was more cautious than you seem to suggest, and just expressing a feeling. This feeling has been seeded through many moments when studying physics, but the strongest one by far is QFT. In QFT you start from very neatly defined state operators in terms of a given coordinate time, write down the Heisenberg evolution equation, and formally solve it in terms of creation and annihilation operators in momentum space. Because Dyson's formula imposes on you a time ordering, you get a sequence of products. For one of these terms, e.g.: \[a\left(a^{+}\right)^{2}aa^{+}a^{3}a^{+}a\] What's the next thing you do before you engage in any calculation at all? Well, you re-define your exact solution to be "better represented" by the normal ordering: \[:a\left(a^{+}\right)^{2}aa^{+}a^{3}a^{+}a:\overset{{\scriptstyle \textrm{def}}}{=}\left(a^{+}\right)^{4}a^{6}\] If nothing else, to me, that very strongly suggests that there's something deeply problematic about time. It may be possible that sequencing of concepts might have consequences, logical consequences, that we simply cannot get rid of within our present system. I'm not saying that every mathematical statement we make has time impregnated in it, but I'm saying that it may well be that we are quite incapable of totally escaping the non-trivial consequences of having a sequential language. Don't pay too much attention to what I'm saying. Maybe I'm just sounding people out about my deepest intellectual insecurities, that's all.