KJW

That's actually the point I'm making. It can't be completely random because then there would be no ability to control. But it can't be completely deterministic, either, because then there would be no free will.

In classical electrodynamics there are no magnetic monopoles. Mathematically, the divergence of the magnetic field is zero. This means that at all locations, there is no source of the magnetic field (unlike the case of the electric field for which the source at a given location is the charge density at that location). Equivalently, this also means that for every hypothetical closed surface, the net flux of the magnetic field through the surface is zero (unlike the case of the electric field for which the net flux through the surface is the total charge enclosed by the surface). A pole exists where there is a surface through which the net flux of the magnetic field is in one particular direction. But because there are no magnetic monopoles, there is always a balance of north and south magnetic poles on any closed surface.

And the notion of free will seems to rely on enough determinism to allow control but also enough randomness for there actually to be free will.

No, they're neurotransmitters. I did work them out a while ago (I actually have this album), and IIRC, the top-left is dopamine, the top-right is serotonin, the bottom-left is glutamic acid, and the bottom-right is part of an endorphin molecule.

So, is he going to bring back leeches?

Her favourite music is the 2017 Bubblemath album "Edit Peptide":

Normal coordinates can be used to prove Riemann tensor identities such as the second Bianchi identity, but they need not be used to prove such identities. I prefer not to use normal coordinates to prove such identities, but to prove them directly. Even though the Christoffel symbols are zero in normal coordinates, the partial derivatives of the Christoffel symbols are generally not zero and the Riemann tensor is generally not zero. The Christoffel symbols are not tensors whereas the Riemann tensor is a tensor. Thus, whereas the Christoffel symbols can be coordinate-transformed to zero at a point, the Riemann tensor in general can't be coordinate-transformed to zero at the point. The Riemann tensor may be defined in terms of parallel transport of vectors around infinitesimal parallelograms. Although the resulting change in the vector is itself infinitesimal, the Riemann tensor that is obtained as a result is not infinitesimal.

Two things: (1): Over cosmological distances, gravity-bound systems are but mere specks. (2): The standard FLRW model is just that... a model. It is a simplified approximation of the actual universe. However, it should be noted that it is superior to consider deviations from a simple model than to use a complicated model from the outset.

For one thing, there's the central limit theorem.

Google was reluctant to provide useful information about what chlorine dioxide powder is, but I did manage to find a Safety Data Sheet for a particular brand of the powder. It turns out that it is a mixture of sodium chlorite and sodium bisulfate. Given that these two react in solution to form chlorine dioxide, it is understandable why the powder should not be premixed in a small volume of water. https://horticentre.co.nz/wp-content/uploads/Safety%20Datasheets/Exstinkt%20Pure%20(Ixom)%20SDS.pdf

pfft

One problem is that G isn’t determined to a very high precision 6.67430(15)×10^-11 m^3/kg s^2 The limitations on that would affect any system relying on it. Yes. But what I said was a continuation of the hypothetical notion mentioned earlier of being able to measure G to an accuracy and precision comparable to that of h and c. Indeed, one of the reasons I said I don't know how to design the measuring instrument is because I don't know how to measure G to the required accuracy and precision. Bear in mind that the reason for replacing ΔνCs with G, apart from philosophical ideality, was to address the concern raised by @Killtech that the current definition of the second is based on an electromagnetic notion (the Cs atom). No, there is no such problem as the fundamental constant cannot be measured in this situation and therefore must be defined. This is fine because the constants - or more precisely the core physics they originate from - serve as the rulers to measure everything with. for example the speed of light together with the other constant allows you to construct a real photon emission which wavelength is fully determined by the constants and this base wave lengths servers as a ruler to compare any other real length to. For this we only need to know the defined values of the constants instead of measuring them. The definition via constants has the nice advantage that we have some freedom in constructing the ruler we use - yet all the different rulers constructed in this way will still agree (if the physical laws underlying them use are indeed correct). I take responsibility for the possible misunderstanding here. Even though the fundamental constants are defined to have definite numerical values, measurements of the dimensions still require physical access to the fundamental constants. Therefore, all the issues associated with measuring the fundamental constants in the past when the fundamental constants were measured still apply to the measurement of the dimensions in terms of the numerically defined fundamental constants today. In particular, the accuracy and precision of measurements of the dimensions is limited by the accuracy and precision of measurements of the fundamental constants even though they are not being measured in the same sense that they were in the past but as a standard of comparison. Why do you think that there is a "true" value of the fundamental constants? Yes, the Planck length is a definite interval of spacetime, but without a unit of length to compare it with, the Planck length can't be specified. And if the Planck length is the unit of length, then the Planck length has a value of 1, but its interval of spacetime remains unspecified.

From: https://xkcd.com/3073/

What NASA level computer did you use Why do you think such simulations require a lot of computing power?

Hmm, it could be but it would require some other constant to lose its definition. The unit of G is composed of units of time, length and mass. It makes no sense to compete for the first two, so its would compete with Plancks constant to define the Kilogramm by its value. As only the value of one of them can be defined, the value of the other becomes a derivative as a consequence. No. Considering the dimensions of the fundamental constants, [math]c[/math], [math]h[/math], and [math]G[/math], one has the following system of equations: [math]c = \dfrac{L}{T} \ \ \ \ \ ;\ \ \ \ \ h = \dfrac{M L^2}{T} \ \ \ \ \ ;\ \ \ \ \ G = \dfrac{L^3}{M T^2}[/math] Inverting this system of equations, one obtains expressions for the individual dimensions in terms of the fundamental constants: [math]L = \sqrt{\dfrac{h G}{c^3}} \ \ \ \ \ ;\ \ \ \ \ M = \sqrt{\dfrac{h c}{G}} \ \ \ \ \ ;\ \ \ \ \ T = \sqrt{\dfrac{h G}{c^5}}[/math] Therefore, specifying the numerical value of each of the three fundamental constants, [math]c[/math], [math]h[/math], and [math]G[/math], is sufficient to define the units of each of the three dimensions, [math]L[/math], [math]M[/math], and [math]T[/math]. Mathematically, it doesn't matter that none of the units are defined in isolation of the others. That is because the three fundamental constants are independent, and thus their expressions in terms of the three dimensions are invertible. However, there is the practical issue of measuring length, mass, and time in terms of the corresponding expression in terms of the fundamental constants. I'm guessing that because such an instrument would have to be able to measure the three fundamental constants, the same instrument would be used to measure length, mass, and time. However, I have no idea how to design such an instrument. [Note: If the LaTex above doesn't render, please Refresh this page]

And measles. Admittedly, I grew up at a time when pretty much every kid got measles, so I am also inclined to downplay the danger. But I have no issues with vaccination, so the measles I had as a child is no reason for the children of today not to get vaccinated.

I've simulated the Second Law of Thermodynamics and the Quantum Zeno Effect on an Excel spreadsheet.

Like when Volodymyr Zelensky met with the King shortly after Trump and JD Vance berated him in the Oval Office.

How is an atom a bound state of the field characterised by c? It's being used to define time. It should be noted that the choice of the particular atom and the particular transition is for technical reasons and not for anything that could be considered fundamentally theoretical. I'm quite sure that if the gravitational constant could be measured to an accuracy and precision comparable to the Planck constant and the speed of light in a vacuum, then it would also be defined to have an exact numerical value as the definition of the second.

There is a housing crisis in Australia, and this is being exacerbated by immigration. The fundamental problem as I see it is that there are going to be winners and losers regardless of what the government does. Increasing the supply of housing will reduce the cost of housing, which will be beneficial to those seeking to buy, but detrimental to those who have already bought. And even left-wing politicians may have a disincentive to implement a policy that goes against their own self-interest.

This is a questionnaire sent by the Trump administration to Australian universities receiving US funding: https://www.documentcloud.org/documents/25595847-questionnaire-for-us-research-partners/

There's a myth in Australia that the conservative party is better at managing the economy. The opposition party tried playing that card, but they got nothing. All they could do was to try to blame the government for the cost-of-living crisis and claim that they would be better able to deal with the Trump administration. Interestingly, the government's response to Trump's tariff was to not impose a reciprocal tariff which would hurt Australians and unlikely to benefit Australian exporters.

The reason why the speed of light in a vacuum has a value of 299,792,458 metres per second is because we have defined a unit of length called "metre" and a unit of time called "second". If instead we define a unit of length called "metre" and a unit of time also called "metre", then the speed of light in a vacuum would have a value of exactly 1. The constancy and invariance of the speed of light in a vacuum is a consequence of the notion of spacetime. Lightlike trajectories in spacetime satisfy in all coordinate systems the expression: gpq dxp dxq = 0 This equation expresses the notion that there is an equivalence between timelike distances and spacelike distances which allows the same unit to be applied to both. But we don't use the same unit for both because a metre of time is an inconveniently small unit of time.

Vegemite is good on buttered toast, but don't spread it too thickly. You're not in Canada are you? There's a bit of a dispute between Australia and Canada over Vegemite (apparently in Canada, there's a law against fortifying food with vitamins, which has led to Vegemite being banned but not Marmite for whatever reason).

If one looks at the Schwarzschild metric, it is obvious that the speed of light seen from spatial infinity appears to be [math]c(1-\dfrac{2GM}{c^2r})[/math], but locally it is still c. And considered in terms of proper distance and proper time, regardless of where the observer is, it is still c. Also, have you checked the deflection of light given by the above? Is it the correct value, or half the correct value. If you only consider gravitational time dilation, you'll only get half the correct value. The full value also includes the curvature of space (the Schwarzschild metric).