IngoBlechschmid

16 ms·

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by IngoBlechschmid 4y ago
I am sorry, I was being sloppy there. There are several systems of axioms we can use to base mathematics on. A common such is ZFC, Zermaelo–Fraenkel set theory with the axiom of choice. Among its axioms are assertions like "there is a
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by IngoBlechschmid 4y ago
By Gödel incompleteness, the fundamental axioms of mathematics actually don't quite pin down the world of mathematics the way we would perhaps like them to do. As a consequence (also a result by Gödel), there are actually many worlds o
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by IngoBlechschmid 4y ago
I generally agree, and want to add that you are not powerless. You can band together with others and then create political wind for the change(s) you desire. Many (most? all?) important changes in society were the direct result of people or
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by IngoBlechschmid 4y ago
> For example, ZFC+CH might non-constructively predict that some machine M halts, while ZFC+notCH might predict that M does not halt. In general, this can happen, but not with this particular choice of example: If ZFC+CH proves that some
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by IngoBlechschmid 4y ago
I agree, and want to add that I feel that NIMBYism would decrease if the residents (as opposed to huge corporations) would earn the profits from those renewable energy farms. You think differently about a wind park at the horizon if you kno
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by IngoBlechschmid 4y ago
When politicians argue in favor of this kind of CO2 reduction measures, targeted at individual citizens, know that they are (perhaps unconsciously, perhaps because of dependence) following the framing put forward by fossil fuel companies:
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by IngoBlechschmid 4y ago
Here you can interactively explore the 4d mother of the Mandelbrot fractal and all its Julia fractals: https://rawgit.com/MatthiasHu/FractalsWebGL/4d/page.html
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by IngoBlechschmid 4y ago
Try the proof assistant Agda without installation directly in your browser: https://agdapad.quasicoherent.io/ Or Lean: https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_g...
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by IngoBlechschmid 4y ago
This puzzle also exists in a transfinite version, where the two players converge on the correct solution but require longer than infinity for the process: http://jdh.hamkins.org/cheryls-rational-gifts/
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by IngoBlechschmid 4y ago
The same police unit (for "state protection") previously raided Tor activists in Augsburg: https://torservers.net/blog/2018-07-04-zwiebelfreunde-raid/
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Cock comment leads to crackdown on climate activists(archyworldys.com)
11 points by IngoBlechschmid 4y ago|9 comments
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by IngoBlechschmid 5y ago
Working category theorist here. I wouldn't subscribe to that statement in this strong form, even though I am convinced that various flavors of type theory are a better foundation for mathematics. But this feature doesn't make me d
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by IngoBlechschmid 5y ago
Out of curiosity, where would you rank the climate crisis on this list? It has already irrevocably caused the extinction of lots of species, and while certainly humans will continue to live, "modern humanity" will be replaced by s
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by IngoBlechschmid 5y ago
Yes, you are right! In fact, to people working in foundations of mathematics it is routine to compile away any explicit use of the golden ratio in Conway's proof and thus obtain a proof which only refers to the integers. However the re
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by IngoBlechschmid 5y ago
Another is Conway's Soliders: A variant of peg solitaire, it takes place on an infinite checkerboard. The board is divided by a horizontal line that extends indefinitely. Above the line are empty cells and below the line are an arbitra
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by IngoBlechschmid 5y ago
Indeed, this is the correct comment to make!
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by IngoBlechschmid 5y ago
Indeed. Here is an animation of the cumulative emissions starting 1750: https://www.youtube.com/watch?v=jx85qK1ztAc The US come in first, my home country Germany takes the fourth spot.
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by IngoBlechschmid 5y ago
Here is a version which can be played by up to three persons sharing a keyboard: https://www.speicherleck.de/iblech/stuff/chaosspiel-2015/cha... Developed as part of a mathematics day for children, the worksh
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by IngoBlechschmid 5y ago
> Slow transfer speeds This used to be case, but in my experience is no more. I'm routing all my traffic over Tor and don't feel slowed down the slightest.
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by IngoBlechschmid 5y ago
The earnings of the CO2 tax could be equally distributed to all citizens on a monthly basis. That way, while consumer prices would increase, all those citizens who contribute below average to the country's CO2 emissions (and those are
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by IngoBlechschmid 5y ago
The big picture is the following: There is a certain kind of groups called "solvable groups". There is a theorem stating that a polynomial equation can be solved by radicals if and only if its Galois group is a solvable group. And
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by IngoBlechschmid 5y ago
Indeed! And in fact, there are set theorists who argue that the traditional dream solution to the continuum hypothesis, adopting new axioms, is doomed to fail, and that we should instead embrace all models of set theory, all possible univer
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by IngoBlechschmid 5y ago
I get your point, and it is valid, but also observe that there have been numerous successful social movements in the near and longer past! They had to fight against vastly more powerful systems and still succeeded in the end. As activists,
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by IngoBlechschmid 5y ago
For this reason, I decided to make Agda playable in the browser here: https://agdapad.quasicoherent.io/ Enjoy! :-)
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by IngoBlechschmid 5y ago
This is not quite true, Gödel's incompleteness theorems can luckily be formalized in extremely weak fragments of Peano arithmetic such as primitive recursive arithmetic (PRA) with its very limited induction principle. :-) The only posi
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by IngoBlechschmid 5y ago
Sorry, I didn't want to argue against a straw man. You are right. I just wanted to indicate that in mathematics, we are much more often in such generic situations than in programming. Accordingly, I wanted to argue that the increased b
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by IngoBlechschmid 5y ago
Working mathematician here. Generally I concede. However I'd like to add that often in mathematics, we are discussing very generic situations. For instance, we are not talking about the radius of some specific circle, which perhaps sho
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by IngoBlechschmid 6y ago
In 2019, just about 10 % of the global electricity came from nuclear power. Hence replacing fossil sources by nuclear would entail large-scale construction of new nuclear reactors. However, we then run into the problem of peak Uranium (our
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by IngoBlechschmid 6y ago
Relevant qntm.org short story about "MMAcevedo, also known as Miguel, [...] the earliest executable image of a human brain": https://qntm.org/lena
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by IngoBlechschmid 6y ago
Yes, you are quite right, but the community around Lean's standard library heavily focuses on classical mathematics.

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