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kurlberg commented on Busy beaver hunters reach numbers that overwhelm ordinary math   quantamagazine.org/busy-b... · Posted by u/defrost
xelxebar · 5 days ago
Pentation? How quaint. For other Large Number fans, David Metzler has a wonderful playlist that goes way down the rabbit hole of the fast growing hierarchy:

https://www.youtube.com/playlist?list=PL3A50BB9C34AB36B3

Highly recommended.

Almost all of these mind-bogglingly large numbers are built around recursion, like the Ackermann function, which effectively has an argument for the number of Knuth up arrows to use. Then you can start thinking about feeding the Ackermann function into that slot and enjoy the sense of vertigo at how insane that becomes.

I find it fascinating how quickly the machinery of specifying large numbers probes the limits of what's definable within the mathematical systems we use.

kurlberg · 5 days ago
If you have a child who likes math I highly recommend "Really Big Numbers" by Richard Schwarz. Tons of nice illustrations on how to "take bigger and bigger steps".

"Infinity is farther away than you thought."

kurlberg commented on FreeBSD for hi-fi audio: real-time processing, equalizer, MPD and FFmpeg   m4c.pl/blog/freebsd-audio... · Posted by u/m4c-pl
bluGill · 7 months ago
Audiophile's are famous for spending a lot of money on "snake oil" to get results that objectively cannot be heard and then claim the sound is better. Sometimes the sound is better, but the human ear cannot tell (lab equipment can). Of even the best lab equipment cannot find a difference.

Good enough if you are happy is good enough. Maybe you can do better in ways you can hear, but with "Flac is my source, decent DAC, decent cans" you are probably getting close to the edge of what the human ear can hear anyway (assuming good audio in that Flac, and the DAC/cans really are decent as you claim)

kurlberg · 7 months ago
I recently got into making some sort of budget hifi setup, and found audiosciencereview.com quite helpful - a good amount of reviewed gadgets with focus on measurements. Ended up with kali lp-6v2 speakers and a SMSL SU-1 dac. Please don't tell me I screwed up. :-)
kurlberg commented on OpenWrt 24.10.0 – First Stable Release   openwrt.org/releases/24.1... · Posted by u/pm2222
TMWNN · 7 months ago
I use the Merlin firmware for my Asus router. I've long heard of OpenWRT but do not know how they compare.
kurlberg · 7 months ago
I have used merlin for quite a while, mostly happy (except for some security holes...) However, once asus drops support for older devices (e.g. rt-ac68u and rt-ac86u), merlin might also drop it. For now rt-ac68u is dropped by merlin, but ac86u is fine for now (at least until the end of the year.)

Upshot: if you care about very long term support, openwrt is nice.

kurlberg commented on OpenWrt 24.10.0 – First Stable Release   openwrt.org/releases/24.1... · Posted by u/pm2222
blackeyeblitzar · 7 months ago
Is there a recommended hardware and step by step guide for those new to this? Can you do mesh networks?
kurlberg · 7 months ago
Based on reddit [1] and other some other recommendations I got an asus ax4200 and put openwrt on it. I'm fairly happy, but some people have run into connection dropping (possibly due to ISP power saving resulting in link dropping down to 10 mbs, and something then goes wrong.) With forum help [2] I found a workaround: either turn off auto negotiation (works) or using a lan port as a wan port (have not tried).

1:

https://www.reddit.com/r/openwrt/comments/1cr1lvp/is_the_asu...

2:

https://github.com/openwrt/openwrt/issues/14192#issuecomment...

kurlberg commented on Convolutions, Fast Fourier Transform and polynomials (2022)   alvarorevuelta.com/posts/... · Posted by u/clearprop
kurlberg · a year ago
There is a nice picture of the "best" for different ranges of sizes of numbers to be multiplied at

http://gmplib.org/devel/log.i7.1024.png

More context and explanation can be found at: http://gmplib.org/devel/

BTW, I like Bernstein's survey of different multiplication algorithms at

https://cr.yp.to/papers/m3.pdf

(there is a unifying theme about using ring isomorphisms to explain many of the "standard" routines.)

kurlberg · a year ago
PS: if you're interested in multiplying "ludicrously large numbers", Harvey and van der Hoeven had a nice breakthrough and got multiplication down to "FFT speed" (n*log(n)), see

https://hal.science/hal-02070778v2/document

A pop-sci description can be found at

https://theconversation.com/weve-found-a-quicker-way-to-mult...

kurlberg commented on Convolutions, Fast Fourier Transform and polynomials (2022)   alvarorevuelta.com/posts/... · Posted by u/clearprop
nickcw · a year ago
In libgmp I think the numbers have to be around 100,000 bits or 30,000 digits for FFT to be faster.

https://gmplib.org/manual/Multiplication-Algorithms

GMP has lots of other methods in between schoolbook multiplication and FFT multiplication. A nice one is Karatsuba multiplication which is very easy to understand and delivers O(n^1.58) rather than O(n^2) performance. Python uses this method for multiplying large numbers together

https://en.wikipedia.org/wiki/Karatsuba_algorithm

kurlberg · a year ago
There is a nice picture of the "best" for different ranges of sizes of numbers to be multiplied at

http://gmplib.org/devel/log.i7.1024.png

More context and explanation can be found at: http://gmplib.org/devel/

BTW, I like Bernstein's survey of different multiplication algorithms at

https://cr.yp.to/papers/m3.pdf

(there is a unifying theme about using ring isomorphisms to explain many of the "standard" routines.)

kurlberg commented on Making AI better at math tutoring   blog.khanacademy.org/why-... · Posted by u/gnicholas
jimhefferon · a year ago
Please, what does this mean?
kurlberg · a year ago
Check out "Diamond Age" by Neal Stephenson.
kurlberg commented on How to generate uniformly random points on n-spheres and in n-balls   extremelearning.com.au/ho... · Posted by u/egorpv
porphyra · a year ago
Another way to generate uniformly random points on a 2D disk that the author forgot to mention: let A be an n x n complex matrix whose elements are iid copies of a fixed random variable with unit variance. Let lambda_i be its ith eigenvalue, and let x_i = 1/sqrt(n) real(lambda_i) and y_i = 1/sqrt(n) imag(lambda_i). As n approaches infinity, the distribution of x, y approaches almost certainly to the uniform distribution over the unit disk.

Tao, T., Vu, V., and Krishnapur, M. (2010) Random matrices: universality of ESDs and the circular law. The Annals of Probability. 38(5) 2023-2065.

kurlberg · a year ago
It's very inefficient, both on terms of runtime and in terms wasted entropy.
kurlberg commented on Please Use ZFS with ECC Memory (2014)   louwrentius.com/please-us... · Posted by u/rdpintqogeogsaa
g0xA52A2A · 3 years ago
I hate this headline and wince every time I see it, even the article quotes

> There's nothing special about ZFS that requires/encourages the use of ECC RAM more so than any other filesystem. If you use UFS, EXT, NTFS, btrfs, etc without ECC RAM, you are just as much at risk as if you used ZFS without ECC RAM. I would simply say: if you love your data, use ECC RAM. Additionally, use a filesystem that checksums your data, such as ZFS.

And goes on to say

> I have nothing to substantiate this, but my thinking is that since ZFS is a way more advanced and complex file system, it may be more susceptible to the adverse effects of bad memory, compared to legacy file systems.

kurlberg · 3 years ago
This has been discussed on HN some times before. User xornot looked at the zfs source code and debunked it, for more details see

https://news.ycombinator.com/item?id=14207520

kurlberg commented on Signed integers are asymmetrical   borretti.me/article/signe... · Posted by u/zetalyrae
high_byte · 4 years ago
I wonder if negative zero is redundant or actually has some uses.
kurlberg · 4 years ago
Yes, it has uses. E.g., see Kahan's "Branch Cuts for Complex Elementary Functions, or Much Ado About Nothing's Sign Bit", copy available at

https://people.freebsd.org/~das/kahan86branch.pdf

(he gives an example regarding complex branch cuts and fluid dynamics applications.)

u/kurlberg

KarmaCake day210September 23, 2012View Original