151–160 of 178 posts
It always fascinated me how basically two quarks, one electron and some bosons can create so much chemical complexity. It feels like trowing just 6 types of lego bricks into a huge bag and after a lot of random mixing obtaining whole universe of diversity.
All the complexity of computing comes from just two bits. (Some even argue that’s true of the universe itself)
A nice 'visual' illustration of the threshold is found in Percolation theory https://en.wikipedia.org/wiki/Percolation_theory where if you have an infinite grid of square rooms with either a wall or a door between each pair of rooms, that there is shift about what is connected when the percentage of door gets just over 50% as is visualized in this animation: https://en.wikipedia.org/wiki/Percolation_theory#/media/Fil…
I recommend everyone interested in percolation theory to also check https://meltingasphalt.com/interactive/going-critical/ and play with critical thresholds interactively!
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It does an okay job, but there are still a lot of unanswered questions, or assumed knowledge for a lay person: > Mathematicians want to know when such a graph is likely to have some sort of interesting structure. Why? > a Hamiltonian cycle, a chain of edges that passes through every vertex exactly once > adding more edges to a graph that already contains the property will not destroy the property. Adding one edge aft…
> Adding one edge after the exact number of edges required to create a Hamiltonian cycle (number of edges equal to number of vertices) would appear to break the property. A Hamiltonian cycle is a simple cycle (no repeated vertices or edges) that contains every vertex of the graph. If a graph G has a Hamiltonian cycle, then adding more edges to G will not make that cycle go away; it will still be there. So the propert…
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Lemme go through details, not because anyone doesn't know the details, but to get them written down and discussable. "Random" means I draw up a list of all possible outcomes. The probability of an event is defined as the fraction of outcomes in which that event is true. Example. Choose two numbers "randomly" between 1 and 3. What's the probability that the two numbers are equal? The list of outcomes is: (1,1),(1,2),(…
Thank you, my original comment was for ELI5, I was asking because I didn't know and clarifying like this helps. Wouldn't it be more correct to say arbitrary instead of random?
Example of a tricky situation: Say we play cards. You shuffle the cards well, and you don't show them to me. I might say the order of the deck is random, to indicate that I have no idea which card is in what position. But you might be looking at the faces of the cards. In that case you might say the same cards are ordered in a way that's not random.
Could we describe the same situation using the word arbitrary but not the word random? I'm not sure. Seems likely.
I know how to make up models and test the models by experiment. I don't know whether randomness is real or not. I don't think it's deeply meaningful what words we use, as long as it's clear what the math is and how we're applying it.
I notice that most links on physics, astronomy and math cover pre-prints. Would it not be prudent to wait for the final version. Is all the peer reviews and "fact checking" done prior to the preprint?
Whether a paper is on a preprint serve is not a big deal. If a lot of experts are excited about it, that’s a story anyway.
And if it falls apart later due to some surprise flaw… well that is also a story!
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All the complexity of computing comes from just two bits. (Some even argue that’s true of the universe itself)
Except there’s no such thing as bits on the hardware level. There’s voltages. High and low. That’s usually 5V and 0V, respectively.
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And yet people will shit on DEI efforts. Incorporating more folks into the scientific endeavor helps combat things like stagnation in science precisely because it reduces academic incest.
DEI efforts discriminate against Asians like Jinyoung, so yes, I will shit on them.
(I am an Asian male, so I really have nothing to selfishly benefit from promoting DEI efforts)
Jinyoung Park's Path to Math video on IAS is a really wonderful 3 minute story of how she came to study threshold behavior in random discrete structures, just like this work. Highly recommended. https://www.ias.edu/ideas/paths-math-jinyoung-park
Math is one of those fields where there seems to be a clear correlation betwixt youth and creativity. It's just the consequence of having fresh eyes looking at an ancient problem ;) But experience is clearly necessary due to the shear vastness of the topic. I find history and philosophy of math to be just as engaging and often crucial. Understanding the origins of probability in 17th century gambling houses, for exam…
Science, baby!
What level of expertise is this proof accessible to? Could a final year undergraduate understand this perhaps with a bit of help or background reading? I am talking about reading and understanding it, not necessary validating the correctness.
Any paper, any field, if you can get your hands on it, Take a half an hour and read the words. Look at the pictures, Look at the graphs. Take a break. Go for a walk, maybe get some coffee, and decide if you want to continue. This will give you a very rough survey of the terrain. Often, I'll quit right here if there's nothing for me to latch on to.
Take a couple of hours, take notes about the things you don't understand - maybe take a minute here or there to look up concepts, maybe take a minute there to graph equations.
Get a good night's sleep. Look at your notes and think about all the stuff you don't understand. There are plenty of things I don't get _at all_. There are also things I can latch onto. Put some serious effort into linking the equations with the words. Decide if you want to spend days or weeks really digging in and _understanding_.
I find each step rewarding. I often quit early, and move on to the next shiny new thing. There's some real value in each step. I learn about things I never new existed. I certainly can't explain them, but sometimes things pop up again and again and I do get the motivation to take a deeper dive - not necessarily mastery, but at least an understanding of my depth of ignorance. Maybe watch a lecture on that topic for perspective.
You never know what's going to be useful. Nurture that spark of interest. You might get nothing out of it today, but 10 years from now, you'll see some other problem and vaguely recall this is kinda like that other thing I never really got. There's definitely some opportunity cost. But if you're just farting around on reddit, an hour here and there can be really enjoyable, and possibly someday useful.