jostylr

10 ms·

61.
by jostylr 2y ago
I think Norm Wildberger's videos are very useful to think about and enjoy though certainly one should reflect carefully on what he says. His videos inspired my work on a new definition of real numbers. The basic idea is that it is the
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by jostylr 2y ago
That is a great paper. I came up with my own definition of real numbers [1] and using the simplified cut property of that paper was a pleasant pathway to establishing completeness. [1]: https://github.com/jostylr/Reals-
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by jostylr 2y ago
It is equivalent to Dedekind cuts as one of my papers shows. You can think of Dedekind cuts as collecting all the lower bounds of the intervals and throwing away the upper bounds. But if you think about flushing out a Dedekind cut to be use
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by jostylr 2y ago
I have been working on a new definition of real numbers which I think is a better foundation for real numbers and seems to be a theoretical version of what you are doing practically. I am currently calling them rational betweenness relation
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by jostylr 2y ago
If one embraces rational intervals throughout, they can be the computational foundation and the ux could have the option of displaying the interval for the complete truth or, to gain an intuitive sense, pick a number in the interval to disp
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by jostylr 2y ago
EPR demonstrated that if you insist on locality and experiments having results in accordance with quantum predictions, then there must be pre-existing elements of reality that determine the results. Bell demonstrated that pre-existing elem
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by jostylr 2y ago
Guesstimation of the numbers is not promising. The article mentions 1 to 3 million as targets, let's say 2 million as an asset at retirement. At 4% withdrawal, that gives 80k a year. Median wage is about that. There are about 4 million
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by jostylr 2y ago
The important point for me is that the equivalence for Cauchy sequences are part of the definition of real numbers as Cauchy sequences. This ought to imply that one has to be able to decide equivalence of two sequences for the definition to
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by jostylr 2y ago
The intuition of a sequence is that the terms get closer to the convergence point. Looking at the first trillion elements of a sequence feels like it ought to give one some kind of information about the number. But without the convergence i
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by jostylr 2y ago
US President number 45 returns, kind of seems like squaring applies.
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by jostylr 2y ago
1225: ten years earlier, Magna Carta starting to limit monarchs and the seed of individual freedom 1681: eight years later was glorious revolution with a bill of rights, marking individual freedoms 1764: ten years later, beginning of Americ
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by jostylr 2y ago
The equivalence class of Cauchy sequences is vastly larger and misleading compared to those of integers and rational numbers. You can take any finite sequence and prepend it to a Cauchy sequence and it will represent the same real number. F
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Engineers 3D print sturdy glass bricks for building structures(news.mit.edu)
6 points by jostylr 2y ago|0 comments
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by jostylr 2y ago
That was enjoyable. You could submit this to the summer of math exposition: https://some.3b1b.co/
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by jostylr 2y ago
The claim would be that prices rise, offsetting the cost to the consumer who are also workers. It does not do much if that is how it shakes out. The stated hope of those arguing for the raise is that the people at the top of the company mak
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by jostylr 3y ago
Article states 4 trillion in excess profits. US government had about a trillion in deficits before the pandemic then spiked up to about 3 trillion in each of 2020 and 2021 [1]. That is a bump of 4 trillion dollars suddenly over those two ye
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by jostylr 3y ago
Do you have any good recommendations for a serious dive into the trade-offs for a socialist/communist system and comes out pro-socialist, one that takes into account the analysis of Austrian economics as well as the historical tragedie
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by jostylr 3y ago
Because there was a basic set of primitives that could give rise to almost an infinite number of possibilities. Multiple paths and iterative forces leads this to a very diverse and thriving evolutionary landscape. It has become gloriously m
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by jostylr 3y ago
The medical system is not grossly unregulated. It is not centrally regulated in DC though there is a lot of regulation from there. It is states and localities that regulate it. For example, in some places, a medical professional can add an
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by jostylr 3y ago
It depends on whether one is referring to the date (see you July 4th) or the holiday (Can't wait for the 4th of July). Though I do think the date version might be becoming more common than the holiday version. As for why the month com
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by jostylr 3y ago
Scott Santens has written and accumulates a variety of resources about UBI: https://www.scottsantens.com/ One old post from him is a detailed plan for paying for it: https://www.scottsantens.com/how-to-refor
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by jostylr 3y ago
At Sudbury schools, reading naturally occurs for students, but the age ranges from 4-12, with typical being 7-9. There seems to be little correlation to early reading and a love of reading, anecdotally from these schools. In fact, often th
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by jostylr 3y ago
That article is a truly marvelous article and very worth reading for anyone interested in either continued fractions or rational approximations. For those who are curious, a simple algorithm for generating these good approximations and cont
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by jostylr 3y ago
We also cannot represent all natural numbers or rational numbers in a computer. But the ones we care about, we generally can. I guess one question is whether there are uncomputable numbers that we need to compute for some purpose other than
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by jostylr 3y ago
I did not mean physically. I meant, having it explicitly written out in a way that rational numbers can be. If I write 3/4 + 1/2, I can compute out 5/4 and that is infinitely accurate. If I want to compute pi + e, an infinite
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by jostylr 3y ago
Yes. The basic reason is lazy evaluation and answering the primary question most people care about when using an actual real number in a computation. The lazy evaluation is that defining the real number is about having a way of answering th
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by jostylr 3y ago
In part, it is about framing it. The oracle approach is not the set of all rational intervals containing a real number, but rather it a rule that acts on a given rational number. You cannot literally hand over a set of all rational interval
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by jostylr 3y ago
I think having a language that helps understand those limitations is a useful achievement. Much of mathematics does have that. A notable exception is the definition of real numbers. They are usually presented as a string of infinite decima
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by jostylr 3y ago
In particular, scan past the data in that example and you will see things like @keydown.down="if(selectOpen){ selectableItemActiveNext(); } else { selectOpen=true; } event.preventDefault();" which tells you what is happening r
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by jostylr 3y ago
As someone who adores alpinejs and is just getting into LiveView, can you explain was this removal a preference to minimize or for an alternate syntax or is there an important reason, such as if there exist conflicts between LiveView and Al

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