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Have we ruled out trolling as the cause of the problem? Anyway, it seems that nearly everything can change- everything except Farid's mind.

Here’s a another approach. We are all made of atoms. Even when I lose an arm or leg, the parts of me that remain are still made of atoms, too. In that sense, I’m the same. However, I am definitely different than I was before when viewing my body as a whole. Parts of me are the same. Other parts are different. My best guess here is that you’re mixing reference frames and believe you’ve stumbled on some profound truth, but to the rest of us you just look a bit confused.

Or in other words: using time t’ from the primed coordinates to calculate a distance x in the unprimed coordinate system assumes Newtonian physics and Galilean transformations.

Exactly. We’re taking a weeks trip to the local lake distric right after Greece. I’m counting on resetting and hopefuly getting new firmware for whats comming in September.

„Kos” island in a multiple pool, private beach and all inclusive hotel presumably with a bunch of other families with kids. I’m already hating myself for doing this but we got a 3 year old so regrettably this is not going to be a dedicated adventure and exploration trip. I wonder for how long I will be able to hold my urges to go and do something stupid, we’ll see...I need good reads to stay a good boy.

No. Space-time should not be comprised of anything like dough. It is not substance-like at all. The concept of space-time is just the recognition that the measurements of space and time are frame dependent and not absolute. The analogy is that in Newtonian physics, space and time are treated like North/South vs. East/West. In such a situation everyone, no matter what direction they are facing, all agree on these directions. Everyone, for example, agrees that town A is 40 miles North and 30 miles East of town B. However the Space-time manner of treating this is that each person uses his own sense of Left/Right and Front/Back. Thus one person facing one direction will say that town A is 30 miles to the left of and 40 miles in front of town B, while someone facing in another direction would say that town A is 50 miles directly to the right of town B. It makes no more sense to think of space-time as being "substance-like" than it would to think of Left/Right-Front/Back as being "substance like". Now I also realize that in GR, it is said that Space-time "curves" in the presence of mass. And to many people this implies space-time being a "structure or substance". This is not what this means. "Curvature" of space-time really just means that the geometry rules governing it are non-Euclidean. In other words, the rules of plane, Euclidean geometry just don't hold.

I'm not sure that would be the case; yes you can push a big mass and it will keep moving, but you need to push against something to start and stop that big mass. Having gravity and friction are actually very helpful to moving and processing stuff - I think doing useful work in microgravity will be more difficult, not less because of their absence. And of all the processing steps for mining and refining most materials, the moving stuff around part is likely to be the least energy intensive part of the whole exercise. I would expect a lot of energy intensive processing just to make (and recycle) the raw ingredients needed for metal refining. I am presuming energy will be some kind of fusion power - ie fusion that is simple enough that a small colony with limited economic and industrial capabilities can build and operate reliably, entirely with local skills and resources - no small step for getting that I am thinking. Fission is technically easier but fissionable elements are not abundant and will probably be mostly contained at very low concentrations within nickel-iron - and 'minimal amounts of energy' looks unlikely to be sufficient to refine it; energy costs of making energy using fission look like a serious issue in such conditions. I've thought the 'stepping stone' approach is the most reasonable of the various virtually impossible ways we might use to get people to another star - if truly self-sufficient colonies capable of spawning new self-sufficient colonies can be successful using asteroid/comet materials, and each new colony is in the direction of a target star, then potentially, eventually, some distant descendants might get there. But except for the very last of that long line, the stepping stones will only be a step to another stepping stone; the people involved aren't going to that star - and if their lifestyle works they don't need to - so keeping society wide commitment to that far, far distant end goal may prove difficult to sustain for the thousands of generations needed. I suggest the urge to find new territory - a primitive urge - underlies the sense of attraction people have for other stars and other worlds, but given the multi-generational nature of the goal, that is really not going to be sufficient to expect whole populations to repeatedly make economic sacrifices for something they will not see. That urge to up stakes and hit the road when things get tough in search of some place better is too vague and non-specific as a motivation, and is not (I think) sufficient for circumstances where you have the ability to make the 'someplace better' yourself, even if from such dismal and difficult raw material as asteroids and comets. Having worked hard and made some comfort and security - if you have successfully built someplace better and the way forward involves sacrificing that hard won security and comfort for starting all over again - that commitment to the far off end goal will be hard to keep going.

A contradiction is when you propose that a sentence is true, but a sentence that says the opposite is true too. Now there are all kind of situations, especially when vague concepts are used, where this is not quite unproblematic. But if you take the concepts precise, then two such sentences cannot be true. Now imagine that the sentence says something about empirical reality, e.g. 'that car is black'. Then it is impossible that the sentence 'that car is not black' is true at the same time. (The vague concepts here could be 'oh well, it is nearly black'.) Simply because the car cannot have 2 colours at the same time (no, no, that the lights are red does not count.) Now say we have a theory, from which it follows that that car is black and is not black. What can you conclude about the real colour of the car? Exactly nothing: such a theory is worthless. As a principle: if we can deduce from a set of supposed truths a proposition, and also exactly the opposite of that proposition, then at least one of our supposed truths is obviously no truth at all. So we can use the principle of contradiction (or better, non-contradiction) to see if: at least one of our propositions was wrong or I made an error in my logical argumentation So you can use the principle of contradiction to prove if some set of propositions can be true together or not. But then, how could you prove if the principle of non-contradiction is correct? Formally, I think you can't. But practically it is impossible to see how it could be invalid.

Intuition would be to minimize non-diagonal segments, so AjkC (However it's easy to add bad diagonal paths that would break the strategy.)