Leaderboard

Because the transfinite ordinals and cardinals are not real numbers. The subject of the thread is "The geometry of the real number line." That's YOUR topic, right? So we are discussing the real numbers. The transfinite ordinals and cardinals are fascinating in their own right, but have nothing to do with the real numbers. In fact the transfinite ordinals (and the cardinals, which are technically a proper subclass of the ordinals) do not intersect the real numbers at all. The transfinite ordinals and cardinals are neither subclasses nor superclasses of the real numbers. They're just a completely different subject. If you are trying to understand whether there's a largest number in [0,1), it's no help to think about transfinite numbers, since transfinite numbers are not in that interval at all. Does that make sense? Besides, haven't you already said you are only interested in the standard real numbers? Why are you suddenly interested in mathematical objects that are NOT standard real numbers? This para does not make sense. First, we can't use transfinite numbers in a discussion of the reals, because transfinite numbers are not members of the real numbers. We can of course use transfinite numbers to talk about the cardinality of various subsets of the reals, but that's not what we're talking about here. Ah. Well, the length of a single point is zero. The length of [0,1] is 1, and so is the length of [0,1). The addition or deletion of a single point makes no difference when we're calculating the length of an interval. I'll keep my clothes on if it's all the same to you, thanks. The length of a point is zero, so adding or deleting a point can not make any difference in the length of a line segment. I think what you are saying is that the intervals [0,5] and [5,6] both contain the number 5, and that is correct. I don't see how that helps you to find a largest number in [0,1). So the two intervals would "bang into each other" at the point 5. You are correct that 5 is an element of both intervals. But as a point, the number 5 has length 0. The two facts are both true. 5 is a point on the real number line and it has length 0. So yes, two points of zero length can still bang into each other, if you want to put it that way. Remember, Newton showed that you can reduce gravitational calculations to "point masses." So if it helps, you can think of them that way. They are points with zero dimensions, zero length, and zero volume, but they still pack a punch. I'm not saying that's any kind of mathematical argument, but if it helps you to resolve this particular objection, I'm ok with it. In your imagination. But the proof that there is no largest number in [0,1) should cause you to realize that your intuition is flawed. It should give you a better intuition. Now there is nothing wrong with having such a faulty intuition. Pretty much everyone has faulty intuitions about the real numbers before they see these technical discussions. But now that you've seen a formal proof that there is no largest number in [0,1), you should be willing to realize that your intuition is faulty, pre-mathematical as it were, and you should update your intuition. What exactly about the proof are you still unconvinced about? I asked you that in my previous post. It's no good for you to say you're unconvinced, without saying exactly what aspect of the proof you are unsure about. If you could focus on the proof we could discuss that. I can't discuss onions or bodies of water or vague pre-mathematical notions of the real numbers. It's more helpful to focus on the actual math. We are not going to discover a largest number in [0,1), because we already proved a few posts back that there is no such thing. Now I'm confused. Didn't you see and more or less agree with the proof I already posted? There is no largest number in [0,1). Proof: Suppose you claim that x∈[0,1) is the largest number in that set. Take half the distance between x and 1 , namely 1−x2 and add it to x , giving: x+1−x2 You can see that we have the strict inequality x<x+1−x2<1 so that x is not the largest number in [0,1) after all. Since x is entirely arbitrary, we have just shown that there is no largest number in [0,1). You have already seen this proof, and more or less said you agree with it. But now you are saying "Are you sure there are proofs?" You already saw the proof. Yes, I'm sure there's a proof, I've now stated it twice. And you've agreed to it. So I have no idea what you mean by asking if I'm sure there's a proof. Ah ... ps ... you said, am I sure THEY are proofs. Are you asking if the proof I gave is actually a proof? Yes, I'm sure. If there is any part of it you are unsure of, I wish you would ask about it or say which part you find unconvincing, so that we can focus on that.

I urge you to look at the derivation of time dilation. Without that as a common base, there is no discussion. And it just leaves you criticizing a theory you aren’t familiar with. I also note that you haven’t defended your claims at all, but expect me to defend a strawman of your fabrication. Which law of physics requires time to be the same in all frames? I stand on the shoulders of giants, who developed the ideas. Unfortunately they can’t understand them for you. ! Moderator Note We aren’t discussing your diagram here. That discussion is taking place in your thread

I can sympathize with the apparent helplessness felt by the Russian families, but I would have more respect as well as sympathy for them if they condemned the Russian invasion rather than suggest it be done in a different manner. “They are prepared to serve their homeland but according to the specialization they’ve trained for, not as stormtroopers. We ask that you pull back our guys from the line of contact and provide the artillerymen with artillery and ammunition.” https://www.cnn.com/2023/03/12/europe/russia-mobilization-putin-protest-wives-mothers-intl-hnk/index.html

How would we know what the properties of space-time actually are ? Is it flat, curved or inside-out ? Remember, I'm in the camp that claims Physics does not tell us what 'reality is, only how it behaves ( see Physics and 'Reality' thread ). All we can say for sure, is that the mathematical model, including geometric curvature, makes extremely accurate predictions about gravity, and how test masses behave when affected by it. Anyone who claims to know more about the actual 'reality' is simply confused and deluding themselves.

Yes, they are similar, IMHO.

I know, I know. That's why I could never be a teacher.

The chopper shares the Earth's momentum. As does everything on the planet. If you jump high on a trampoline at the equator, the trampoline and yard doesn't shoot away from you at 1000 mph (460 m/s) and drop you a few blocks to the west. Galileo's boat is a helpful google search.

This is a strange question, let's look into it further. If you take a helicopter and and hover above the surface - what do you mean ? If you take a helicopter and hover above the helipad for 12 seconds, 12 minutes, 12 hours or 12 days you will still be abov the helipad and not above the other side of the world. If you fly the helicopter so you have some forward or backwards speed we distinguish two speeds Ground speed And air speed The ground speed is of course zero when you are hovering over the helipad. But the airspeed is only zero in 'still air'. Still air means the air is actually turning with the Earth at the same rate as the ground. Otherwise it needs to be enough to counteract the tendency of your craft to move along with the wind and then needs to be some more if you actually want to go anywhere. However the Earth's rotation does play a part since the flying time London to New York is 8 hours, Whilst the flying time New York to London is only 7 hours. Is this actually the phenomenon you are actually thinking of ?

It sounds more like a computer game world than the one I'm living in.

My attitude is that if you show up intending to discuss physics - in a context that you are challenging mainstream physics - you should have sufficient knowledge to do so. I shouldn’t have to explain the basics to someone who is not asking that the basics be explained. It’s interesting that you object to not having a mechanism for time dilation but not to having none for time. You are misusing what is meant by a preferred frame, and apparently, causality.

In one word, inertia. Bodies continue moving at a constant speed and in the constant direction unless something disturbs that movement. For example, if you throw something up while moving inside a car, the thing will go up and down into your hand despite the car's moving forward.

It seems to me that there are many areas where the expected effects of the project rely on believes about human psychology. This is an extremely weak point, I think. It didn't work out well in previous attempts. For an historical example, there was an assumption that equal gender rights will eliminate prostitution. Needless to say, it didn't happen. There also was an assumption that if working people are the owners of production means and products, they will not steal, cheat, etc., but will rather be involved in increasing the effectiveness of their work. The large-scale result was quite opposite. There was an assumption that people will be driven by a common good if they know that they are equal part of that common. Didn't work. Etc. OTOH, negative aspects of human psychology were used historically very effectively. Fear, hate, belonging, etc. This is a problematic approach: how this proposition can be tested? There is no objective test? This is not scientific. PS. Trial-end-error is kind of test, too. But in this case the error might be very painful.

It's worth noting that Newtonian forces were 'eliminated' by Hamiltonian and Lagrangian formulations of mechanics.

Say we start at x = 1/2. Then repeating the "half the distance" idea gives 3/4, 7/8, 15/16, 31/32, ... We get an infinite sequence of points, each one a little closer to 1, but none of them is the largest in [0,1). This is vague. Numbers aren't "attached to" each other as if by velcro for example. Didn't the two-dimensional example of the boundary of a circle help? Sometimes geometric intuition is helpful. Sometimes it's confusing. What is the formal definition of [0,1)? It's [math]\{x \in \mathbb R : 0 \leq x < 1\}[/math] That denotes the set of all real numbers greater than or equal to 0, and strictly less than 1. There's no "attachment" in the math. Just a set of real numbers. By the way this is set theory notation, since you mentioned Zermelo-Fraenkel. The curly brackets denote a set. The colon is read, "such that." The boldface [math]\mathbb R[/math] stands for the real numbers. So the notation literally denotes "The set of all real numbers x such that" etc. This analogy doesn't work for me. For one thing, water isn't the real numbers. Water is made of discrete molecules and exists in the physical world; while the real numbers are a mathematical abstraction that, as you note, form a continuum. But even on its own terms, the water analogy doesn't work. If you zoom in to the "surface" of a body of water, you find a cloud of molecules that aren't part of the body of water, but are in the process of evaporating into the air. In fact the surface of a body of water very nicely models an open set with no boundary at all. The surface is fuzzy, with molecules constantly jumping around and some of them escaping into the surrounding air. I don't understand it either, as shown by my example of zooming in to the "surface" to see a cloud of molecules leaving the water and evaporating into the air. There is no well-defined surface of a body of water. Now perhaps you are thinking of surface tension, but still, the analogy is strained. If you zoom in, you see molecules bouncing around. You can never point to any one collection of molecules and say, "That's the surface." Before you're done speaking, some of those molecules have evaporated into the air.

I think C would be the best one to start with. But then maybe it would be cooler to continue with Rust.

Yes, agree. Another +1 to @wtf. The sad part is that here are 100 posts, and 0 progress.

A lot of politics has happened in that time. Today's physicists use the word "geometry" as a rhetorical bludgeon to shut people up when they complain about the unscientific nature of relativity as a metaphysical principle. "It's just a matter of geometry". Baloney! Geometry is mathematics, and math is description. It doesn't explain anything or rule out things having some kind of substantive implementation. The word "define" is confusing here. Anything can be defined. Definitions are just relationships between ideas and words. The point is that geometry can only describe, and it's scientifically absurd to say that things happen with no implementation. Saying that something can't be a "fabric" because it's a "geometry" is a rhetorical BS tactic, and referring to "magic wands" in the same post is hypocritical.

I tried to take baby steps earlier on by looking at Neutrino and later on at Z boson,so that I bring the Fuller picture which is huge but short,then I was afraid not to be swallowed by blackhole(the recycle bin of speculation). Spacetime fabric here is being created,where our Special relativity and General relativity can take place, Virtual particles are not the 'the virtual particles, virtual photons' which come later on in quantum foam and quantum fluctuations when planck's 'microscope' start resolving things. Dark photons they are under primodial quantization 'then a Full stop' beyond the standard model,cause our ''planck's 'microscope'' can't resolve them. About hot and dense those are properties,a longside with frequency that are explainable. There is no issue of 'ether' here I fear that a lot.Its all about the Model.In this case special relativity and General relativity is highly regarded.But go beyond by explaining even the rotation curves of galaxies and cosmic web ( the cosmic voids sorrounding cosmic filaments).too much. Emptiness you happen to know that it's there because your are conscious,I doubt if you were dead even us you left behind could be able to describe what you are and have become. I know the diagram because my imagination fits there,No.Thats not the purpose,just take the scientific knowledge you have and use the diagram as a template if it doesn't fit there then am done.scientist keep complaining about similarities across different subjects/discipline,how don't we know consciousness I just everywhere? Thanks alot for the response so far I thought the black hole will swallow me,my cries down there are being heard....hhhh...Hawking radiation at least keep escaping. you