KJW

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).

It's a good day to be an Australian. Some time ago, I posted an example of an evil policy of the previous right-wing government of Australia. Although it wasn't part of the election campaign for this election, I did hear it mentioned that the opposition party wanted to reintroduce this policy. It's a relief that they didn't win. It's also a good day for the rest of the world. It shows that sanity still exists in the world. Australia has people who like Trump... a disturbingly large number of them, actually. There was even a party called "Trumpet of Patriots" (the name says it all). But in spite of that, the majority of voters decided that it was best to keep the power of government with the left.

Although the counting is incomplete, the election has been decided... the Australian Labor Party has won what has been described as a landslide victory. The leader of the opposition party has lost his own seat in parliament. The election result was quite unexpected. The recent polls suggested that Labor would win with a reduced majority or even a minority government (requiring support from other parties or independents). But instead, they increased their majority.

Australia went to the polls today to elect their next federal government. The polls have closed, and counting of votes is still in progress. However, the current trend suggests that the Australian Labor Party (the major left-wing party) will retain government. Thank you, Donald Trump. About six months ago, the polls suggested that the people were not happy with the current government due to the cost-of-living crisis and were looking to change government. But it seems to me that what is happening now in the US is causing people to shy away from right-wing parties. This may be the one beneficial thing Trump has done for the world... to be the example of what not to vote for.

They are also used in face recognition. See: https://en.wikipedia.org/wiki/Eigenface

Than what?

I think it needs to be clarified precisely what a clock measures. A clock (specifically the part that physically responds to time) measures proper time along the spacetime trajectory (aka world line) of the clock. Ideally, a clock is not affected by any form of motion or gravity. This is a consequence of the principle of relativity, the principle that the laws of physics (and therefore the behaviour of clocks) are the same in all frames of reference. It should also be noted that, according to the equivalence principle, a local gravitational field behaves like an accelerated frame of reference. This means that gravitational time dilation is the same as time dilation in an accelerated frame of reference. It also means that freefall in a gravitational field is locally the same as an inertial frame of reference (btw, this means that special relativity is an important part of general relativity, not merely a precursor of it). A device that receives signals from a remote clock is not itself a clock. It is merely relaying to the observer of the device the measurement of proper time along the spacetime trajectory of the remote clock. Suppose the remote clock is ticking exactly once per second. It will tick exactly once per second irrespective of where it is or how fast it is moving. The intervals in spacetime marked by the ticks will be genuine one second intervals (I feel I can't stress this enough). Observing the remote clock involves null geodesics in spacetime from each tick of the remote clock to the observer, the time interval between the observed ticks being measured by a local clock. The interval between the ticks at the location of remote clock is exactly one second, the interval between the observed ticks measured by a local clock need not be one second. Both intervals are proper times at their own locations, but in no way is the interval between the observed ticks a measure of time at the remote clock. Nor is the interval between the observed ticks of the remote clock a measure of local time. What is coordinate time? Coordinate time is the value of a particular coordinate of a particular type of coordinate system. If spacetime is sliced into spacelike three-dimensional slices, coordinate time identifies each spacelike slice. The spacelike three-dimensional slices are usually considered to be defined by hypothetical observers whose spacetime trajectories are normal to the spacelike three-dimensional slices. The coordinate time may be the proper time for one particular spacetime trajectory. If the spacetime is stationary, then this coordinate system is naturally defined by the isometry between the spacelike three-dimensional slices. In the case of a black hole solution, the t coordinate corresponds to proper time at spatial infinity. If the spacetime has a Friedmann-Lemaître-Robertson-Walker metric (FLRW), then the t coordinate is the proper time everywhere (the age of the universe), but only for trajectories that are at rest relative to the comoving frame of reference.

Mrs Tilly likes spectral yellow but not RGB yellow.

It appears that one can "Like" by clicking the heart but not "Downvote" if someone has already upvoted or downvoted a post.

Around the turn of this century, I devised such a theorem. Basically, any dictionary based only on words must contain words that are either undefined or circularly defined. One way around this is for a dictionary to also contain pictures. In the case of defining a clock in terms of instructions on how to build it, one also avoids the problem associated with a dictionary based only on words.

Some time ago, I came up with the perfect definition of a clock. Note that the definition of time is that which is measured by a clock, so the definition of a clock cannot reference time. But one can define a clock without referring to time by providing instructions on how to build a clock. The instructions to build a clock is the definition of that clock.

We are always at a speed of zero relative to our own frame of reference. It should be noted that speed (or velocity) is always relative to something. However, the speed of light is always the same in all frames of reference.

I don't know what "opposite of the speed of light" means. However, (according to Wikipedia) the peculiar velocity of the Sun relative to the comoving cosmic rest frame is 369.82 ± 0.11 km/s towards the constellation Crater near its boundary with the constellation Leo.

Mrs Tilly believes in God but does not believe in religion.

When you refuse dialogue, it's only your loss, really 🤷‍♂️

Perhaps you can elaborate on how f(x) is continuous. It is clearly a discontinuous function to me.

@exchemist I've been looking at N-methyl-2-pyridone as an analogue of the N-substituted cytosine. The 1H-NMR spectrum has the following chemical shifts: H3 = 6.17 H4 = 7.34 H5 = 7.32 H6 = 6.57 HMe = 3.59 (https://www.chemicalbook.com/SpectrumEN_694-85-9_1HNMR.htm) Compare with benzene = 7.34 (https://en.wikipedia.org/wiki/Benzene_(data_page)) Compare with trimethylamine = 2.12 (https://docbrown.info/page06/spectra2/trimethylamine-nmr1h.htm) Compare with tetramethylammonium iodide = 3.207 (https://www.chemicalbook.com/spectrumen_75-58-1_1hnmr.htm) Compare with HMe of toluene = 2.32 (https://en.wikipedia.org/wiki/Toluene_(data_page)) Compare with HMe of methylcyclohexane = 0.858 (https://www.chemicalbook.com/SpectrumEN_108-87-2_1HNMR.htm) The chemical shifts of the ring protons of N-methyl-2-pyridone, being similar to benzene, do suggest a ring current associated with aromaticity. I also compared the methyl protons of N-methyl-2-pyridone to the protons of the methyl group attached to the uncharged nitrogen of trimethylamine and the charged nitrogen of tetramethylammonium iodide. However, this is complicated by ring current effects which led me compare the methyl protons of toluene and methylcyclohexane. On thing worth noting is that the oxygen atom of phenol and especially of the phenoxide ion is electron-donating to the 2, 4, and 6 positions. This is similar to the tendency for N-methyl-2-pyridone to be in the pyridone electronic configuration. Similarly, pyridine and especially the pyridinium ion is electron-withdrawing from the 2, 4, and 6 positions, also leading to the tendency for N-methyl-2-pyridone to be in the pyridone electronic configuration. However, I suspect that N-methyl-2-pyridone is still aromatic.

Given the resonance structures N–C=O <—> +N=C–O– , even with the deoxyribose attached the cytosine ring should still be aromatic (and flat).

For some reason, your LaTex is rendering for me immediately without hitting Refresh, but other LaTex I've looked at still requires Refresh.

Looking at the image in @studiot 's post, one thing that I see is notable is that whereas cytosine enolises to an aromatic hydroxy compound, the attachment of the deoxyribose to the nitrogen atom "freezes" the molecule in the non-aromatic keto form.

LaTex requires me to hit the Refresh button in order for it to render.