Paul Erdos famously swore by their productiveness.
From Wikipedia:
His colleague Alfréd Rényi said, "a mathematician is a machine for turning coffee into theorems",[31] and Erdős drank copious quantities. (This quotation is often attributed incorrectly to Erdős,[32] but Erdős himself ascribed it to Rényi.[33]) After 1971 he also took amphetamines, despite the concern of his friends, one of whom (Ron Graham) bet him $500 that he could not stop taking the drug for a month.[34] Erdős won the bet, but complained that during his abstinence mathematics had been set back by a month: "Before, when I looked at a piece of blank paper my mind was filled with ideas. Now all I see is a blank piece of paper." After he won the bet, he promptly resumed his amphetamine use.
This is great and I will use it right up until it starts showing ads. I really hope Google can find another income stream because ads are a deal breaker for me. The first time Google maps dropped two pins on a location search, one an ad, was the last time I used Google maps.
If you were able to construct a rigid beam 25 million miles long wouldn't you be able to transmit data (push a button) on the other end faster than the speed of light?
It is impossible to construct a perfectly rigid beam, in the sense that you are thinking of. A "rigid beam" would be made up of matter and, as you push on one end, you would trigger a wave that would propagate from neighbour to neighbour until it reaches the other end.
Nope. Pushing on the end of the beam sends a pressure wave through the beam. The button gets pushed when the wave reaches the other end. Wave travels significantly slower than light.
What you're proposing is an effect mediated by physical forces. Specifically, on a fundamental, atomic level your beam is made up of atoms. And when you push it, you're bringing atoms closer together, that feel an electrostatic repulsion. And the beam moves.
So, in the best case, this method of communication is equivalent to communicating with electromagnetic waves. And they have a speed limit: the speed of light :)
So this wouldn't be faster than light communication.
Even if you create a rigid beam (ignoring the fact that it isn't possible), once you start turning it with a certain speed, its end will start reaching speed of light and start acquiring mass. As the speed aproaches speed of light, the mass of the beam will be approaching infinity.
To think about it, if you have a sufficiently long beam you won't be able to give it any angular momentum at all, regardless of how much force you apply. It will be fixed in space. Perfect starting point if your hobby is moving stars with a combination of chains and pulleys.
It is possible to conceive of violating the known laws of physics if you start by conceiving of an object that violates the known laws of physics. A perfectly rigid beam 25 million miles long would be such an object.
A beam made of matter is not rigid (as we think of the word) on that scale, as others in the thread have pointed out.
I think that's going a little too far. If you can construct a "rigid beam" five feet long, I see no way that relativity countermands a "rigid beam" 25 million miles long. It's just that "rigid" doesn't mean what grandparent thinks it means -- info still travels through the beam via pressure waves.
The pressure waves are ultimately manifestations of the exclusion principle, expressed through forces that are constrained to travel at or below c.
So yes, relativity dictates that you can't create a rigid beam 25 molecules long, much less 25 million miles long. There can be no such thing as a perfectly rigid beam of any length.
Exactly, you can only construct beams at any scale that seem rigid at some scale. A 2 foot long piece of re-bar looks pretty rigid, until you look closer.
The root of the word chivalry is telling. We portray history in fairy tale manner, as if the old days were better, and consequently it is awkward to feel anger. What about the progress we have made in spite of our naturally selected for violence? Evolutionarily, except in niche cases, pacifist gene lines were subjected to negative selection pressure. We unfortunately have some wiring that is not up to code.
The tragic fact about scapegoating is that once a community has chosen a scapegoat it is very hard for it to "regain its composure."
Who will be the first to defend the scapegoat? There are big disincentives. You risk being grouped with the scapegoat and suffering the same fate. You risk becoming the new scapegoat. You risk reprisals from the folks who are hiding in shadows while the spotlight follows the scapegoat.
And it probably won't even help. Once a person has chosen an opinion, they tend to defend it, and this applies tenfold to a group. (This plays out in social media every day.) Changing a mob's opinion is hard. Time doesn't necessarily help. There are scapegoats that are centuries old.
The social dynamics favor letting the scapegoat take the fall. That's why scapegoating is so common that we have an ancient name for the practice, even though almost everyone would agree that it's immoral.
Everything you say is politically true, but the reason we have judges and juries (in the US anyway, I don't know how Italy works) is that they are in a position to stop the BS.
the reason we have judges and juries (in the US anyway, I don't know how Italy works)
I assure you that Italy has judges and juries and a modern judicial system. This isn't some teeny tribe of Amazonian warriers here, this is a large country.
"The Lives of a Cell" by Lewis Thomas is a tremendous book, pulling back the curtain on biology. Clear, concise and well written, very similar to Feynman with physics.
From Wikipedia:
His colleague Alfréd Rényi said, "a mathematician is a machine for turning coffee into theorems",[31] and Erdős drank copious quantities. (This quotation is often attributed incorrectly to Erdős,[32] but Erdős himself ascribed it to Rényi.[33]) After 1971 he also took amphetamines, despite the concern of his friends, one of whom (Ron Graham) bet him $500 that he could not stop taking the drug for a month.[34] Erdős won the bet, but complained that during his abstinence mathematics had been set back by a month: "Before, when I looked at a piece of blank paper my mind was filled with ideas. Now all I see is a blank piece of paper." After he won the bet, he promptly resumed his amphetamine use.