11–20 of 232 posts
I might have missed it, but is there (or do we know of) a different model for which the velocities actually add? Essentially, how do we go from slopes to angles here?
I love the name of the scientist Al Unapietra. The thing is very well explained, but it's very sad to see it as a twitter thread, which is a mostly unreadable format.
I believe it is harder to write (due to the character limit of each text block), but, far from “unreadable”, I can read it fairly easily.
Why? Because it describes movement as rotation from the infinitely far away point (a special basis vector there). And "coordinates" there are somewhat self-normalizing, because there is a special basis vector that keeps coordinates' squares.
And, of course, it is investigated as a tool to think about relativistic coordinates, linking my comment to a tweet part that says "wrong tools can obscure things".
For example, why do we measure in fractions of light speed? What happens when we are already rotated all the way to light speed and then fire another bullet?
I guess there are other ways to reason about this, but it still doesn't feel intuitive to me.
Summary: For small angles, approximation makes it look like gradients (y/x) add simply (a+b). Similarly low velocity in relativity world makes it look like velocities just add as well. With some insight we discover how it really works, including how the approximation makes it look correct for small values.
I cannot help but add a reference to a conformal geometric algebra here: https://en.wikipedia.org/wiki/Conformal_geometric_algebra Why? Because it describes movement as rotation from the infinitely far away point (a special basis vector there). And "coordinates" there are somewhat self-normalizing, because there is a special basis vector that keeps coordinates' squares. And, of course, it is investigated as a tool to…
Doesn't this also work in normal geometry as the length of a translation goes to zero and the distance to the rotation's origin goes to infinity... because a big circle looks like a straight line up close?
I love the name of the scientist Al Unapietra. The thing is very well explained, but it's very sad to see it as a twitter thread, which is a mostly unreadable format.
Twitter threads don’t bother me. The brain quickly adapts to skipping the irrelevant parts (username, like buttons, etc) and to expecting the cadency of tweets. I believe it is harder to write (due to the character limit of each text block), but, far from “unreadable”, I can read it fairly easily.
But it is literally unreadable to me. I couldn't finish reading the thread and had to find an alternative way out of twitter.
Fist trial, using my android phone with fennec fox. There is a modal that hides the content asking me to "log in"; if I close the modal I go back to the twitter homepage. Thus unreadable because I don't have a twitter account. Sometimes I have managed to read a few tweets by a "smart" combination of closing the successive modals and reloading the page, but not this time.
Second trial, using my laptop with firefox browser and heavy adblocking. I can read only the first three tweets, the rest do not load due to some third-party javascript.
No big deal. Third trial, now I open a "clean" firefox browser session with just ublock origin, and I manage to read about 30 tweets, until it starts talking about hyperbolic rotations. The thread obviously continues, but the sole link below it "show replies" does not work. When I click on it it says "Whoops! Something went wrong. Please try again!".
Typically I wouldn't bother and stop reading. Fuck twitter. But today I really wanted to read this thread because I teach these things. Thus I learned to use nitter, which gives an interface of twitter that, even if it's equally ugly, it sort of works (in that you can actually manage to read the text).
In retrospect, this is an extremely sad state of affairs. We have an excellent article which is made of a short text, a few simple formulas, and a few simple images. This could be a static html page of a handful of Kb with img tags. But it is a slow and humongous javascript monstrosity that does not even work, and may disappear at any time if twitter "bans" this user for reasons unrelated to this text.
I like this, but it doesn't completely remove the "unintuitivenes" of relativity. For example, why do we measure in fractions of light speed? What happens when we are already rotated all the way to light speed and then fire another bullet? I guess there are other ways to reason about this, but it still doesn't feel intuitive to me.
I like this, but it doesn't completely remove the "unintuitivenes" of relativity. For example, why do we measure in fractions of light speed? What happens when we are already rotated all the way to light speed and then fire another bullet? I guess there are other ways to reason about this, but it still doesn't feel intuitive to me.
You can’t rotate all the way to lightspeed, that would be rotation by an infinite angle. For any finite angle (i.e. speed below c), you can always add the angle of the bullet to get a new (finite) angle.