michel123456

You're welcome.

William Shanks. "The pinnacle of hand computation of π was achieved in the nineteenth century. William Shanks was a mathematician who spent a great amount of time compiling logarithm tables, prime number tables, and the like; in the days before calculating machines, large tables of such values were essential for work in engineering or physics. He did try his hand at π, using Machins formula, and in 1873, after many years of labor, presented 707 digits of the number. But π can be a cruel and fickle muse. It was later discovered that Shanks had made a mistake, and that after the 527th digit, his calculations were wrong. Nevertheless, it was the best value of π available until the advent of high-speed digital computers." from here

You need a ruler.. You are using centimeters. You will draw at scale 1/50. It means each meter in reality will be drawn on paper 1/50 of it: 2 cm. (100cm/50=2 cm). 2 cm on paper=1m in reality. 1 cm on paper=50cm in reality 1mm on paper=5cm in reality. And 5cm in reality=1mm on paper 10 cm in reality=2mm on paper Your drawing will fit on a regular sheet of paper A4. If the room is small (a bathroom for example), you can work at bigger scale 1/20 At that scale, 1meter in reality is 5cm on paper. 1cm on paper is 20 cm in reality. 1mm on paper is 2cm in reality. Does that help? Usual scales are 1/500, 1/200, 1/100, 1/50, 1/20, 1/10, 1/5, 1/1 for large buildings or plots (1/200) to detailed plans (1/20). Other intermediate scales are sometimes used according to the profession. You can also buy an architect's scale but that may not help much if you are not used to it.

Welcome. Welcome to all the others also. Staff don't welcome here.

Maybe are you exaggerating a little bit. "Although the basic applications and guidelines that make the Internet possible had existed for almost two decades, the network did not gain a public face until the 1990s. On 6 August 1991, CERN, a pan European organization for particle research, publicized the new World Wide Web project. The Web was invented by British scientist Tim Berners-Lee in 1989." from wiki. That was to show your post has been read.

eerg ai

Let's take a rod. A hollow cylinder. Let's put it horizontaly, with a laser device at one end. The rod is standing still at rest. Let's open the laser for a time T so that light travels inside the cylinder a distance D. In Spacetime, light goes from point A to B, having travelled the interval X. Something like fig.1 here below: In this diagram, speed of light, C, is the angle of the line AB. It is expressed as a fraction: meters/seconds. Because we are measuring light, we can pose that [math] D=CT [/math] (1) From the diagram, using Pythagoream theorem, we can pose that [math] X^2 = D^2 + T^2 [/math] (2) Replacing (1) in (2) we get [math] X^2 = C^2 T^2 + T^2 [/math] (3) From the diagram, it appears that X corresponds to the definition of the Minkowski spacetime interval S. Because it is a lightlike spacetime interval, S=0* If we pose that X (from the diagram) is the same as S (from Theory) we get [math] X^2 = C^2 T^2 + T^2=S=0[/math] (4) or [math]C^2 T^2 + T^2=0[/math] (5) which has the only solution [math]C^2=-1[/math] (6) Does that seems correct? * from Minkowski formula here we have [math]x=D[/math] [math]y=0[/math] [math]z=0[/math] [math]t=T[/math] which give [math]S^2=D^2 - C^2T^2[/math] introducing (1) [math]S^2=C^2 T^2 - C^2T^2[/math] which has a null result.

This thread is going out of tracks. To Lemur: please stop. To DH: bad wording do not help and may be interpretated erroneously as lack of arguments. To staff: do something.

What you mean is that probably, following Pythagorean logic, Minkowski made a first try with plus signs everywhere and saw that something was not corresponding to reality. Putting a minus sign solved the problem, and that's it?

Do you mean it is an ad hoc?

Thanks for the link. But still, I don't understand the origin of the negative sign. From your link, this extract: The obvious difference between the green equation & the red one (the Lorentzian) is the negative sign. How was this imported?

Roman propaganda. Which civilization killed 80.000 people in one day?

Nothing. Let air circulate.

For the record: "The word "barbarian" comes into English from Medieval Latin barbarinus, from Latin barbaria, from Latin barbarus, from the ancient Greek word βάρβαρος (bárbaros). The word is onomatopoeic, the bar-bar representing the impression of random hubbub produced by hearing a spoken language that one cannot understand, similar to blah blah and babble in modern English.[citation needed] Related imitative forms are found in other Indo-European languages, such as Sanskrit बर्बर barbara-, "stammering" or "curly-haired". The earliest attested form of the word is the Mycenaean Greek pa-pa-ro, written in Linear B syllabic script.[2] Depending on its use, the term "barbarian" either described a foreign individual or tribe whose first language was not Greek or a Greek individual or tribe speaking Greek crudely. The Greeks used the term as they encountered scores of different foreign cultures, including the Egyptians, Persians, Medes, Celts, Germans, Phoenicians, Etruscans and Carthaginians. It, in fact, became a common term to refer to all foreigners."From wiki. So all civilizations are barbaric to the others. As for violence, all have a part of culpability. I don't know the champion.

I think not. A "Cosmological Time Dilation" as you said is already inside our models. Our unwritten assumption is that time don't change: in this case CTD is equal to unity. Besides, we know that no universal time exist. Objects moving at large speed experience a time different than ours. Each observator has his own time, and following that principle, the Cosmological Time Dilation should not be seen as an actual property of the universe, but as an observational effect. And I think yes. If CTD exists, then indeed observable phenomenas would happen at different durations, and it would greatly alter our calculations. I estimate the dimension of the observable universe would be reduced, and density of matter should increase.

aïe aïe aïe !

In this article of Wikipedia, about spacetime interval, from which I post some extract here below, it is said (in bold the part concerning my question): "After Einstein derived special relativity formally from the (at first sight counter-intuitive) assumption that the speed of light is the same to all observers, Hermann Minkowski built on mathematical approaches (...) (...)In the Minkowski space, one needs four real numbers (three space coordinates and one time coordinate) (...)The distance between two different events is called the spacetime interval. A path through the four-dimensional spacetime, usually called Minkowski space, is called a world line. Since it specifies both position and time, a particle having a known world line has a completely determined trajectory and velocity. This is just like graphing the displacement of a particle moving in a straight line against the time elapsed. The curve contains the complete motional information of the particle. In the same way as the measurement of distance in 3D space needed all three coordinates we must include time as well as the three space coordinates when calculating the distance in Minkowski space (henceforth called M). In a sense, the spacetime interval provides a combined estimate of how far two events occur in space as well as the time that elapses between their occurrence. But there is a problem. Time is related to the space coordinates, but they are not equivalent. Pythagoras's theorem treats all coordinates on an equal footing (see Euclidean space for more details). We can exchange two space coordinates without changing the length, but we can not simply exchange a space coordinate with time: they are fundamentally different. It is an entirely different thing for two events to be separated in space and to be separated in time. Minkowski proposed that the formula for distance needed a change. He found that the correct formula was actually quite simple, differing only by a sign from Pythagoras's theorem: where c is a constant and t is the time coordinate.[Note 2] Multiplication by c, which has the dimensions L T −1, converts the time to units of length and this constant has the same value as the speed of light." My question is: where does the negative sign come from ?

I am surprised that you admit this possibility.

So you were serious. I thought it was a joke. (emphasis mine) ??? what is that all about? Are we in the humor section? Why boring? Your description looks correct to me, but it is only the obvious beginning.

IMHO you must follow a sequence: first find "how", then say "that's the reason why ..." If you go directly to "why" without knowing "how", you are on the wrong path.

I understand nothing. Don't shout. Try to explain better. Are you saying that a point do not exist? because a point has a length?

Palindrome

Sort of. It is the main reason I didn't post this in the other thread. Shortly, my point is: when you play with Time, you inevitably play with Space. Instead of stating "space is expanding" upon the assumption that Time is immuable, you could IMHO state that "time is expanding/shrinking" and get the same observational result.

the error is that the whole cardboard didn't stay in place, it moved in time with us. To see what happens, let's simplify the diagram and look at it from above. It becomes something like fig.b fig.b a year has passed, we have moved in time from A to B. But time has passed for our cardboard as well. The cardboard in position 1 on which we have pinned circle 1 has moved in time and is now in position 2. So we are looking at the same galaxies, they have not moved (in space) and nothing is expanding. All right. But imagine for a while that time for distant galaxy was not the same as time for us. That the 2 T's on the diagram were not exactly the same. Imagine that time was not regular, but exponantial, for example. What would have been our observation ?

This a diagram from another thread fig.2 (see the other threadfor explanation) WARNING in the following diagram & explanations, there is a small intentional error. Just in order to enhance argumentation. The error will be corrected afterwards. Now, for the sake of simplicity, let's forget for a while existing Theories, and say that we are living in a stable Universe where nothing moves & nothing expands. Let's pin all these stars & galaxies on a gigantic cardboard. Now, nothing can move. And let's wait till next year, the same epoch, to see what happened. And here we are, a year has passed, and we look back at our cardboard. What do we see? We see now the same Galaxies and stars that are 1billion year + 1 year away, because our point of vue moved in time one year. Something like fig.a Earth has moved from A to B in one year. It appears from Earth that the same stars & galaxies have moved in space only due to time. They moved from the black circle to the blue one. What happened? Did our cardboard expanded, did space expanded? Or is there a catch somewhere? Of course there is a catch.