Creating something out of nothing: The Banach - Tarski Paradox https://youtu.be/s86-Z-CbaHA
That's a consequence of the axiom of choice, which has historically been a highly controversial axiom.
Ask HN: What is a science fact that blew your mind when you learned it?
181–189 of 189 posts
Re: Ask HN: What is a science fact that blew your mind when you learned it?
#182Earlier quoted context omitted.
Isn't this like saying if X is an axiom and you can prove Y via X, you shouldn't trust Y is true because you can't prove X is true? What systems for determining the truth exist that aren't built on top of some fundamental axioms?
That’s where Gödel’s theorem comes in. There’s always axioms unprovable without expanding the system
Goedel's completeness and incompleteness only apply if the initial set of axioms is powerful enough to express addition over all the integers.
Re: Ask HN: What is a science fact that blew your mind when you learned it?
#183Exactly anything you can think of can be represented as a segment of pi's infinite decimal expansion.
Re: Ask HN: What is a science fact that blew your mind when you learned it?
#184Ok, so maybe not a "fact" but the hypothesis of the False Vacuum: https://en.wikipedia.org/wiki/False_vacuum This quote blew my mind: "The possibility that we are living in a false vacuum has never been a cheering one to contemplate. Vacuum decay is the ultimate ecological catastrophe; in the new vacuum there are new constants of nature; after vacuum decay, not only is life as we know it impossible, so is chemistry a…
You should also read the Three Body Problem trilogy, specifically the last book, although I won't spoil it. It uses a plot device very similar to a false vacuum.
Re: Ask HN: What is a science fact that blew your mind when you learned it?
#185A 2016 poll of 1,500 scientists reported that 70% of them had failed to reproduce at least one other scientist's experiment (50% had failed to reproduce one of their own experiments).
I would love to see this number for computational scientists.
While anecdotal, its easy to run into issues like this[0] where scientist with little CS background assume certain behaviors in code that don't actually exist.
[0] https://www.vice.com/en_us/article/zmjwda/a-code-glitch-may-...
Re: Ask HN: What is a science fact that blew your mind when you learned it?
#186I absolutely cannot psychologically deal with the Monty Haul paradox. https://en.wikipedia.org/wiki/Monty_Hall_problem I've coded it multiple times in multiple programming languages as a cathartic exercise. Despite seeing the results obviously printed out in a console in front of me, I just can't handle it. I lose SAN just thinking about it.
A bit late to the party (came from Hacker Newsletter) but it seems obvious to me:
- If you happen to choose a door with a goat (⅔ of the time), the host has to choose a goat door, leaving "switch" a guaranteed win
- If you happen choose the door with the car (⅓ of the time), the host opens a random goat door and you have 50/50 between staying and switching
So always switching is the correct move - if you do that you'll win the ⅔ of the time (every time you open a goat door).
Re: Ask HN: What is a science fact that blew your mind when you learned it?
#187Electrons in a copper wire do not travel at the speed of electricity. Not even close. Electricity travels at nearly the speed of light. Electrons themselves travel like molasses: "In the case of a 12 gauge copper wire carrying 10 amperes of current (typical of home wiring), the individual electrons only move about 0.02 cm per sec or 1.2 inches per minute (in science this is called the drift velocity of the electrons.…
Actually, 0.02 cm * 60 seconds = 1.2 cm (not inches).
Re: Ask HN: What is a science fact that blew your mind when you learned it?
#188A compressed spring weighs more than the same spring uncompressed. The moon and earth weigh less together than if you weighed them separately and added the values together. Most of the weight of solid objects is due to the high speeds and binding energies of the elementary particles within them rather than the rest mass of the constituent particles. The number of particles that exist is relative to how fast you are a…
> There is such a thing as interaction-free measurements: you can take photos of things without ever letting light hit a detector and you can tell whether a bomb is "active" without actually interacting with the detonator.
Can you provide a link that talks about that? It goes against my understanding of why there's an uncertainty principle at all
Re: Ask HN: What is a science fact that blew your mind when you learned it?
#189That the Amazon soil is actually very poor in nutrients and the dust from the Sahara desert is actually what keeps the Amazon rainforest alive.
Long ago the South American and African continents were one. To think of it, there is still a major connection!