studiot

Let us explore your idea further, starting very simply and building up to see where that takes us. OK so you want to model the spacetime that we live in. So what to work on ? Let us start with a plain and simple set of points. By itself, such a set is not a manifold for manifolds enjoy extra properties than plain sets do not generally possess. In this we have 2 choices. 1) We can consider relationships between our set and other sets, taking the set as a whole. We can roughly equate set properties like this to the physics notion of 'global' properties. 2) We can consider relationships between elements of out set. This can be roughly equated to the physics notion of 'local' properties. Working on the second option Physicists like to introduce a coordinate system here. The advantage of this is that it brings with it the notion of ordering of elements, also called the axiom of choice. But doing this introduces aditional constraints we did not ask for. I will return to this later as this is the path conventional relativity takes and pays the price by requiring additiona equations/functions to define further structure. But the key property we must have is connectivity, because we want to model motion and exchange between elements. In a topological manifold we can do exactly that, so long is it is connected. Most authors make connectivity either an explicit or implied requirements and then say no more about it. But the bottom line is that if A is not connected to B the you an't get from A to B and there is plenty of topologicat theory about such neworks. In fact in relativity there are invariants for what is called 'the interval' between each and every event point in the manifold. So the manifold can be constructed as a network of invariants, fixing the place of each and every element in this network. Such a network does not introduce additional constraints in the way that coordinates do. So I propose to examine the path between two of your nodes or relativistic event point or my manifold called A and B becaue I want them to offer the same results. This is most easily done graphically, but it is too late to start sketching tonight so I will do this tomorrow.

Why haven't you read it ? Though I will say that you have made a better fist of attempting to fractalise Time. However you have not yet succeeded. Your model still has coordinates (x, y, z, t) and therin lies the problem. You realise that for a fractal to exist you require at least ( p + 1 ) dimensions for it to exist in, where p = int(Hausdorf dimension) and p > = 1 ? You are only fractilising time and you have only provided 1 dimension to do this in. that is not enough. The consequence of that deficiency will appear in you nodes and tree structure, as you scale the view. Points that are a node at one scale will not be a node at a different scale, leading to a node jumping around in time. Alternativelly your nodes cannot be considered as point structures.

What makes your time fractal ? We already have a current speculative thread proposing fractal time, but the proposer can't seem to support his claim of fractal time.

That's part of the fun.

How many (English) words can you (without AIs or SEs) think of that have no vowels ?

Interesting. Solving 4 = (1 + r/100)25 tells me that this is a compound annual rate of increase of 5.7%

Just breaking established mathematics .

There you go again invoking fractals, without answering my question. Fractals cannot have tangents. If I am wrong about this I would expect to see a few mathematical lines starting with a recognised mathematical statement such as Derrick's theorem and ending with something like Therefore vector PQ is a tengent of fractal AB

Talking of time Rincewind is logged as posting his last post 6 hours ago on my screen You are logged as answering 2 hours ago and in you quote boxes it refers to /Rincewind's post as 37 minutes previously. How are those timechecks compatible?

Thank you for replying to my other points, if rather obliquely. But what was the answer to this one ?

Cab you please clarify the point of this thread in one simple sentence. Reading through your posts I find a mixture of very good and decidedly bad points so I remain unclear as to what is meant. It may interest you to know of the Mars bar theory. For a very long time, Mars has been recognised a a stable well run company. Economists have used the price of a Mars, over time, bar as an indicator of the value of a currency over time.

A good proportion of passersby these days are glassy eyed and either sporting large 'ear muff' things or talking on phone or throat mike. ☹️

You will also have to expend energy pumping stuff around the system.

Well most parts of the world have a version of good morning / afternoon from guten morgen to bonjour to gdday ...... and leave it up to them to respond or not.

Whilst I can find quite a details of Titan's atmousphere in Thermodynamics of the Earth and Planets - Alberto Patino /douce - Cambridge University Press I cannot find any reference to heavy hydrogen (deuterium) so I would like to clear up a clear up what may be some misconception. 1 Deuterium is also called heavy hydrogen (as in heavy water) because it is ordinary hydrogen with an extra neutron in the nucleus. It's symbol is not H2, ( It is D) which is the hydrogen molecule made from two ordinary hydrogen atoms. None of the compounds named in (b) and (c) are really heavy organics, they are just a bit more massive molecules than methane. But yes, sunlight (UV) and not so strong at Saturn's distance from the Sun breaks down (dissociates) the methane into 'free radicals' (CH3)- and H+. These are highly reactive and so two mehtyl radicals can join together to form acetylene or one methyl and one methane molecule to form ethane, loosing an H- which joins with the other H+ to form a hydrogen molecule. 2 See swansont's answer 3 Yes I understand there is an outer haze that forms which acts in the same way as the earth's greenhouse effect by reflecteing back the longer radiation from the surface (although I'm not sure if this is now longer than infra red), whilst permitting passage of shorter wavelengths in the sunlight.

This also require the following condition. That the space in which the spacetime manifold is embedded (or may be considered to be embedded since you are requiring tangents and invoking the exterior calculus thereof) is either linear or affine. Otherwise calculus doesn't hold. Finally, how do Fractals have tengents ?

It's quite a while now since number or count has been acknowledged as a fundamental physical variable with the same status as mass, length or time etc. I don't know why folks keep ignoring this.

As usual a succinct summary. +1 But we should not forget the implications of the phrase "in their own local frame" which has mathematical and physical implications. The physical ones being that we are basing the origin of this frame on an ideal 'point particle'.

This same 'come on' has been posted on other science sites and leads to some sort of aren't-we-clever electronics gadget club. I didn't stay long enough to see if they charge (money).

Take heart Ptolemy said that. Pope Leo said that Lord Kelvin said that and yet and yet and yet We are still constantly discovering that there is more to discover than we know.

What do you mean by a long stick on a stone (or even a short one for that matter) ? Are you referring to a lever or something else ? Or are you just pulling our legs (stixks) ? FYI there is plenty of scope for 'virtual Physics' for instance the Principle of virtual work, D'Alembert's method and plenty of others.

The first thing to note is that as with any computer system it can only output what it is programmed to output. One of the features of much of human discovery has been the occurrence of the unexpected. Columbus died thinking he had discovered Asia. Fleming died knowing he had discoverd penecillin. Rutherford's famous statement https://spark.iop.org/collections/rutherfords-experiment The quote is from a famous experiment described here and I have referenced it as it describes the sort of process that leads to discovery. That is to be alert for the unexpected. So one possible approach is to program your AI to compare with the expected and output anything that is unexpected. I remember being the only student in the class that got the 'right' wrong answer in a Chemistry experiment when the teachers gave use the wrong solution and everybody else falsified their results to fit expectations.

OK I'll make a start The philosophy of any subject must be able to reach all parts of that subject and thus must include the foundations of that subject. Many subjects go beyond the foundations an usually this involves specialisation into non overlapping sections. But just as you would not build a house that only had foundations under the left but not the right, the foundations of a subject must support the whole edifice. Furthermore the scientific method is only a part of Science. More scientist-hours are spent on the dreary infil between the glory discoveries.

OK I won't look forward to it in the hope it doesn't happen again. 😃

Whyever not ? Is there a difference and if so what is that difference ?