btilly

36 ms·

511.
by btilly 1y ago
It is a theorem that any argument that can be made with nonstandard analysis (NSA), can also be made without it. The question is therefore whether NSA helps people's intuition enough to make it worthwhile. In elementary Calculus, it re
512.
by btilly 1y ago
And that most published majority believed in the Ptolemaic model. Which as https://en.wikipedia.org/wiki/Geocentric_model#Ptolemaic_mod... says: > Ptolemy argued that the Earth was a sphere in the center of the uni
513.
by btilly 1y ago
You can write down any set of hopefully consistent axioms, write down any set of definitions from them, and start proving theorems. The result will be mathematics. But not all mathematics is equally interesting. People who look at asymptoti
514.
by btilly 1y ago
And now you see what I don't like about it!
515.
by btilly 1y ago
Fear that TikTok was doing exactly this was widespread enough for Congress to pass a law forbidding it. Then Trump became President and decided to not enforce the law. His decision may have been helped along by some suspiciously large donat
516.
by btilly 1y ago
The idea that people in medieval times believed in a flat Earth is a myth that was invented in the 1800s. See https://en.wikipedia.org/wiki/Myth_of_the_flat_Earth for more.
517.
by btilly 1y ago
No, it is the case. Look for the comment in the article, after passing to a subsequence if necessary . The ultrafilter produces the necessary subsequence for any question that you ask, and will do so in such a way as to produce logically c
518.
by btilly 1y ago
It would be like a reverse gravitational slingshot, in a different way. There is no way to capture with just 2 bodies - it would have to leave on gthe same hyperbolic orbit that it arrived on. However if it drove by and had a close enough i
519.
by btilly 1y ago
I'm not a big fan of using nonstandard analysis for this. We're assuming the existence of arbitrary answers that we cannot ever produce. For example, which function is eventually larger than the other? (1 + sin(x)) * e^x + x
520.
by btilly 1y ago
We were downsizing from a house to an apartment. A professional crew absolutely cannot, for example, make decisions such as which books can't be kept because we're moving to a smaller space.
521.
by btilly 1y ago
She also was for making Germany economically dependent on gas pipelines to Russia, even though she knew that she was funding Russia's war in Ukraine. I am not inclined to give her a free pass on that.
522.
by btilly 1y ago
When my wife and I moved, we packed up the house over several weeks, decided what went, and what would be left. We then rented the U-Haul recommended for a 3 bedroom apartment, picked two random Mexican volunteers, and paid them more than t
523.
by btilly 2y ago
That is light coming from the accretion disk, and things falling it. The light does not come from the black hole itself.
524.
by btilly 2y ago
We are able to recognize that they are nonstandard because they contain numbers that we recognize are infinite. But there is absolutely no statement that can be made from within the model from which it could be discovered that those numbers
525.
by btilly 2y ago
The only thing that I've seen cited as potential evidence either way is that one neutrino, with an energy too high for other mechanisms that we have thought of. But it is just a single neutrino. And it may be produced by a mechanism we
526.
by btilly 2y ago
> The choice quote from part 1: "[our] final interpretation says that every spacetime is locally approximately flat in the sense that near any point of any spacetime (or near sufficiently small segments of a curve), there exists a f
527.
by btilly 2y ago
First, the idea of describing it that way comes from Veritasium. Take complaints to him. See https://www.youtube.com/watch?v=XRr1kaXKBsU for the video where he does it. Yes I know it is handwavy and misleading. But I consid
528.
by btilly 2y ago
The Schwarzschild solution is the unique distribution in GR for nonrotating mass in a small area, in a universe that is asymptotically flat at a long distance from the mass. This is not a flat universe, but most of it is pretty darned close
529.
by btilly 2y ago
My understanding is that we can rule out having too many really small ones (we'd see them evaporating) and we can rule out too many stellar sized ones (gravitational lensing), but we haven't ruled out black holes in size ranges of
530.
by btilly 2y ago
The Peano Axioms lead to both the standard model of arithmetic (the integers that we want), and nonstandard models. See https://en.wikipedia.org/wiki/Non-standard_model_of_arithmet... . In that article you'll see r
531.
by btilly 2y ago
This only covers stellar black holes. (Note that this black hole is believed to be a stellar black hole.) Those statistics could change quickly if you add to it a currently unknown number of primordial black holes that arose around the Big
532.
by btilly 2y ago
Except that this answer does not make sense. General Relativity predicts that if you fill flat space-time with matter, it will start to contract due to gravity. It is not uniform density by itself that prevented the early Universe from form
533.
by btilly 2y ago
Excellent question. Gravity pulls things in by causing space-time to accelerate in a particular direction. In other words we accelerate towards the Earth at 9.8 meters per second per second because that is what space-time itself does. The s
534.
List of P(doom) Values(pauseai.info)
2 points by btilly 2y ago|0 comments
535.
by btilly 2y ago
There are several ways to make this rigorous. An explicit epsilon-delta style proof is not that hard to produce, it's just a little messy. What you have to do is, for a given x and 0<ε, pick N large enough that you can bound the tai
536.
by btilly 2y ago
While this may convince students, you haven't actually prove that any exponential function has a slope. The usual presentation doesn't even demonstrate that such functions are defined at irrational numbers. That said, it is worthw
537.
by btilly 2y ago
Poor summary. Better summary. Fibonacci hashing isn't a great hash function, but it is a really good solution to mapping large integers to small integers. Using it for that doubles the speed of hashing in practice.
538.
by btilly 2y ago
I strongly agree with this, and particularly point 1. If you ask people to provide estimated ranges for answers that they are 90% confident in, people on average produce roughly 30% confidence intervals instead. Over 90% of people don'
539.
by btilly 2y ago
The case where the precedent was set suggests that it is within the outer perimeter of what the President does to give a speech designed to whip up a crowd before they head them off to the Capitol to attempt a coup. While Trump may go farth
540.
by btilly 2y ago
Binary white dwarf systems can also go supernova, even if the combined mass is not that large as far as stars go.

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