/sci/ - Science & Math

>>14778581
*clap* you used the big word "limit" like the big boys (and girls ;-) ).
Now you just need to learn what it means! We are already halfway at the finish line! Then you get a cookie and can stay up an extra hour this evening! :festive_emoji:
>>14780243
inf - inf is not indeterminate, it's infinity. (inf/inf is honestly a retarded concept/notation.)
(a > b) <=> false
It's truly not easier to dumb down why uncountable infinities are bigger than countable ones than talking about bijections. If you can pair any natural number (apple numbers) to something (e.g. a digit in a notation), it's countable.
But bijection breaks down when the formula kinda incestuously, kinda like an Ouroboros, loops around and applies to itself. Because then, you can't non-arbitrarily pair an element of the domain to (exactly one/any) in the codomain, because you already need another infinite bijection for that.
Think about it like this: a string is recursively augmentable with arbitrary symbols. Countable infinities only use strings of length 1. Uncountable infinities can use ANY string length, including infinite.

Earth provides

>colonists/hookers
>the beginning for ISRU industries like steel mills, habitat excavators, or plastic production lines
>goods that are too much of a pain in the ass to make on Mars, like computer chips, GMO crops, and fuel rods for nuclear reactors
>a ton of telecommuters for everything ranging from coding to psychotherapy because having a guy on earth who communicates with a satellite dish on Mars is way cheaper than having a guy on Mars. Note that the 18 minute delay for speed of light will limit what these people can do

Mars provides

>bragging rights
>scientific discoveries (possibly proof of life on Mars or something cool like that)
>military benefits (space force base on mars could probably do some kind of cool shit
>the ultimate tourism opportunity
>precious metals (you can mine virgin platinum reserves, refine it on mars, and ship that shit back)
>a jumping off point for expeditions deeper in the solar system, such as the moons of Jupiter and Saturn, or mining missions in the asteroid belt
>souvenirs, I bet you anything they make some shitty Martian wine that's fertilized with human feces, and retards buy it for 9001 dollars a bottle

In my opinion emotions are fast-track / shortcut solutions for conscious processes.
Like you can think and dismay about a problem for days but ultimately will likely to end up with the same answer as your emotional answer to it. Being emotional saves energy and provides a fast response in situations. I think this might also be the root of the NPC and female problem. For an animal being emotional works well, but for humans it's becoming less and less effective as complexity increases. Feelings like pain is also an emotion of wanting to stop the cause of pain. If you take your time and think through your situation you might be too late and end up dead. Everyone is emotional on some level, while also having the ability to approach problems on an analytical matter of their choice. Some just use their analytical ability more often.
For an AI the equivalent of emotion would be neural training which is generally achievable with today's technology. Consciousness is a more difficult issue, but might naturally arise after a certain complexity of stimuli is reached to analyze and regulate the response to all the complex input. So far we are nowhere near creating an artificial model matching the insane complexity of the human brain.

>spend huge quantities of resources building giant gyroscopes as foundations for cities
>spend loads of electrical power keeping them spun up
>earthquake happens
>gyroscopes wrench themselves off their housings, everything's fuckt
gyroscopes don't make forces/torques magically go away; they just resist them using their stored energy. if the amount of force is greater than the strength of the materials used to make it, you get a catastrophic failure mode.
don't believe me? take an old xbox and rotate it while it's reading the disc.