u/tfb

Egypt is not really described the way you say it is, and in particular dynasties are a subsidiary division whose closest analogy is probably a royal house of England (or later, of the United Kingdom), such as the Plantagenets, or Tudors. As an example consider the sequence:

• Old kingdom (c2700 to c2200 BCE) comprising third to sixth dynasties
• First intermediate period (c2181  2055 BCE) comprising seventh to part of eleventh dynasties
• Middle kingdom (c2040 to c1700 BCE) comprising eleventh, to part of thirteenth dynasties

First of all this is a thousand years of history: this is a period longer than the time from the Norman conquest to today.

Secondly there's a real difference here. Although we don't know everything about these periods, Egypt was a unified kingdom in the old and middle kingdoms,. while in the first intermediate period it was not: it was two kingdoms divided into two kingdoms, Lower and Upper Egypt which were separately ruled. Eventually upper Egypt conquered lower Egypt and a single kingdom arose.

Finally, as an English person who has lived both in England and Scotland, your view of 'English history' is fairly dramatically wrong. There were some fairly dramatic developments between 1603 and 1707. Welsh and Irish people also might have something interesting to stay here.

I have worked in climate science. Climate scientists understand how their models work, because those models are based on physics & chemistry. Traditionally, weather people also understood how their weather models worked, because those models were also based on physics & chemistry.

But weather prediction (as opposed to climate modelling) does not in fact require understanding of the model: an opaque NN which predicts tomorrow's weather better than a physically-motivated model is a better weather prediction system than the physically-motivated model.

A decade ago it seemed fairly clear to me that, in fact, NNs probably would start being very good weather-prediction systems. I think that's now happening.

That approach doesn't work for climate modelling for the reasons I explained. Worse, many climate models are very closely related to weather models: in the place I worked, the atmospheric component of the climate mode was the weather model, built with different parameters. If opaque NNs start dominating weather prediction this means that climate modelling, which can't (or should not) use opaque NNs, will now have to build its models without making use of existing, well-funded, weather models.

There is a critical difference between a climate model and a weather model which very much influences how they need to be written.

The job of a weather model is weather prediction. Nobody cares how it does this: if I could make a weather model which was demonstrably more accurate than existing weather models using tea-leaves and cat fur, then that model is, in fact, a better model than existing physics-based models.

It is also straightforward to assess the accuracy of weather models: if you predict the weather n hours ahead, then in n hours you know what the weather actually is.

This makes weather prediction a poster-child for neural networks: nobody cares that you predicted the weather with an opaque blob of weights, and you have an endless stream of training data for the system.

OK, so what about climate? First of all, if I make some prediction about the climate in a decade, then people are absolutely going to ask me how that prediction was arrived at. And my answer had better be along the lines of 'we wrote a model based on physics with a bunch of physically-well-motivated assumptions and parameters, and here are its results'. An answer along the lines of 'we have an opaque blob of weights which we trained on past climate, but we have no idea how it works' is not going to be taken seriously. Denialists already don't take climate predictions seriously: this would be giving up.

Secondly assessing accuracy is much harder: if I predict the climate a decade hence, then probably I don't want to wait a decade, while doing nothing which might change the prediction, such as reducing fossil fuel use, to decide if the prediction was correct.

Finally, there is not the firehose of continually-adjusting training data there is for weather: nobody expects a climate model to predict tomorrows weather, you have to wait months-to-decades for training data that is useful.

I hope climate scientists understand this, but I worry they don't.

This does not mean there are not uses for NNs in climate modelling, still less GPUs. It just means the opaque-blob approach is a disaster.

Terminology depends on the domain. In cosmology, and more generally in differential geometry people use the word 'shape' to mean something like 'the rules of geometry'. In normal life we use it to mean something somewhat different.

That's really something you just have to get used to, as it happens a lot. For instance, in normal life you might say that a basketball is a sphere. But a mathematician would say that the surface of the basketball is a sphere: in other words that the basketball itself is a ball, whose boundary is a sphere. Or specifically the baskeball is a 3-ball whose surface is a 2-sphere.

While that might happen, especially as the 'technology' is entirely unspecified, there is another explanation which we essentially know gives rise to black holes: the collapse of massive stars. We have observed massive starts, we have a fairly good understanding of the physics which underlies stars, and we have observed collapse events. And finally, we've observed black holes (in so far as this is possible).

So, well Occam's razor.

No. But if the UK starts having long, dry, hot summers as the climate changes then it also will not be a temperate climate in the sense we're used to.

In particular there's a thing called the Köppen climate classification. England is currently Cfb which means temperate, no dry season, warm summer. It could change to Csb or Csa meaning temperate, dry season, warm summer, or temperate, dry season, hot summer. More extreme changes are also possible.

There's the additional factor that things are changing faster than the system can catch up with: the only times previously where the rate of change is faster as we're currenty seeing are probably impact events and perhaps massive vulcanism. So the grasses that have thrived here stop thriving and it takes too long for grasses which could thrive here to seed themselves. This is particularly bad for trees: new grass can be seeded by humans and grows quickly, while you can't do the same for trees.

Time travel, in the sense of travel into the past, may be allowed by some theories, and certainly is allowed in some artifical scenarios. Long ago I worked causality violation (which is the fancy term for 'time travel into your own past') in one such theory, general relativity. So in that sense yes, people do, or did, work on such ideas.

I would make a guess that almost all such work is trying show that time travel is in fact not allowed by the theories in physically reasonable cases: certainly mine was.

For example, I know the symbol which indicates congruence is three squiggle lines. There is no way to make that symbol.

There is in fact a way to make it. It is U+224B 'triple tilde' You can either pick it from the character picker of your OS (I did this) or select it from a document that uses it.

If you then search for that the Wikipiedia 'conguence' will be a hit. In fact I think ≅ is more commonly used.

Yes, absolutely.

Almost! If there was no other object in the universe than the Earth there would not be. But there are in fact other objects: the Sun for instance. Because the Sun exists and the Earth is in orbit around it, there are various points where the gravitational force of the Sun and Earth balance, and you just sit there.

These points are the Lagrange points and there are 5 of them, named L1 to L5.

• L1 is between the Earth and Sun and it's the point where the Earth's and Sun's gravity are equal and opposite. It is not stable: if you move even slightly away from it you get further away.
• L2 on the Earth-Sun line (like L1) but is further away from the Sun than the Earth is. You can think of it as a point where the combined gravity of Earth and Sun allow an orbit. L2 is also not stable. The JWST is close to L2, and I think the Nancy Grace Roman telescope also it.
• L3 is the other side of the Sun from the Earth, and slightly outside the Earth's orbit. It's also not stable.
• L4 and L5 are 60 degrees ahead and behind the Earth respectively in Earth's orbit. L4 and L5 are stable for the Earth-Sun system (not for all systems: the heavier body needs to be enough heavier than the lighter one).

Note that the Lagrange points all move around with the Earth's orbit.

You can also consider the Lagrange points for the Earth-Moon system, and there are the same 5 points (not in the same place of course).

I am being serious. There are a lot of questions asked by 'people' with hidden profiles on reddit which are very similar to this. I think these are quite likely to be one of the ways the 'AI' companies are getting humans to provide training data for them for free.

Something to notice is that the updating of the main array is entirely serial: all updates to it are protected by the same mutex.

So don't do that: the worker functions should return the array they've created, and then the outer function should smash these into the main array.

Here are (untested!) modified versions of worker and run-thread:

```lisp (defun worker () ;; Compute results into a local array. (let ((array (make-array (* width height 3) :element-type '(unsigned-byte 32) :initial-element 0))) (labels ((help () (let* ((n (create-random-complex-number)) (c (iteration-count n))) (cond ((and (in? n) (out? n) (> c 50) (< c bailout)) (let ((r? #c(0.0d0 0.0d0))) (do ((y n (algorithm y n))) ((or (not (in? y)) (= y r?))) (incf (aref array (+ (colors c) (* (change-number-into-pixel y) 3))))))) (t (help)))))) (dotimes (x sample-size) (help))) ;; Just return the array we made array))

(defun run-thread () (let ((pthreads '())) (dotimes (x 16) (let ((id x)) (push (sb-thread:make-thread #'worker :name (format nil "worker-~a" id)) threads))) (let ((ca color-array)) (declare (type (simple-array (unsigned-byte 32) ()) r)) (dolist (thread threads) (let ((r (sb-thread:join-thread thread))) (declare (type (simple-array (unsigned-byte 32) ()) r)) (dotimes (i (length r)) (incf (aref a i) (aref r i))))))) (draw)) ```

An even better approach is probably to partition things differently: divide the array into disjoint regions, and have worker threads which write into their region. This removes the Amdahl bottleneck, but it assumes shared memory.

'Grass always comes back' is why all deserts are covered in grass. Oh, wait, no.

If you keep stressing it enough (so if there are a succession of very hot summers with not enough rain) then the grass will not, in fact, come back. When it doesn't come back for long enough then we'll start losing the topsoil.

Any n vectors which spans V is a basis for V. That set is also linearly independent and you can prove this. Any n vectors which are linearly independent will span V and thus be a basis for V, and you can prove this.

Just ... don't use some synthetic text extrusion machine: learn the maths.

Cornwall is not the moon, cars work there. Some (many) of the roads are small: don't have a lorry-car, have something that's a sensible size.

We'll also need to train the computer. We could ask questions on reddit to cause a lot of people to provide answers which we could scrape.

Oh.

No, it doesn't. If you can't measure something even in principle then from the point of physics it doesn't exist. You can postulate some unmeasurable-even-in-principle 'universal time' all you like, just as you can postulate some unmeasurabe-even-in-principle hidden variables behind QM and you're just not doing physics at that point.

They do both see each other's clock run slow when they are moving inertially.

The reason the spaceship's clock indicates less time when it returns to Earth is because its frame was not always inertial.

No. Once you have passed the event horizon you reach the singularity in finite proper time.

This is the answer!

I think there's an additional thing which is that the escape velocity for smaller planets is low enough that hydrogen can escape from their atmospheres? I may be wrong about this though.

let z = x - y, then (x - y)<sup>2</sup> + 1 > 0 is z<sup>2</sup> + 1 > 0. You can choose x and y to make z any real number. What do you know about the squares of real numbers?

I don't think I made my point very well, sorry. What I was saying is that theories of physics don't explain things in terms of some underlying mechanism outside the theory: they just say 'here's a mathematical model which you can use to make predictions'. The model is just what it is.

And they have to work like this, because if they didn't you'd have an infinite regress. GR is, for sure, the classical limit of some quantum theory of gravity in just the same way that Newtonian gravity is a limit of GR. (And even if QM didn't exist, GR predicts singularities which is a huge hint that it's not a completely correct theory.) But it doesn't go on for ever (or if it does that would be extremely strange): at some point you reach a theory which says 'here's a model, and that's it'.

To be fair the ancient Egyptians did this as well: hieroglyphic evolved into hieratic which in turn evolved into demotic. I think that rather little of the written Egyptian language was probably hieroglyphs: it's just that a lot of the monumental inscriptions were.

'Exotic matter' means matter with negative energy density, which pretty much means negative mass. You can stop there: anything else is not really worth worrying about.

That's not how physics works. General relativity posits that, loosely, gravity is curvature of spacetime. That's all it does: it doesn't say why spacetime is the way it is or what 'underlying' properties cause this, any more than it makes assumptions that spacetime is embedded in some higher-dimensional flat structure. It just says 'what predictions would I make if the properties were this?'.