one needs to perceive the signal without the noise
the way to perceive the signal is to amplify it by positive recursive feedback, but the noise must be lower than the signal for this to work. that is why we reflect on the self. the signal is from the self, because that is all there is.
it may be possible to filter out some noise
Youtube comments on textbook standard BusyBeaver function introduction https://www.youtube.com/watch?v=kmAc1nDizu0 :
Fun fact: there is a finite number of states in the observable universe. You can estimate an upper bound of the number of states of a system as e^S, where S is the entropy of a black hole with the same size as the system. For our universe this ends up being around S=10^123. This means that we could only ever hope to compute up to BusyBeaver(e^10^123), as later busy beaver numbers need computations that our universe is too small to contain.
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The op proposes to calculate BusyBeaver(e^10^123), so e^10^123 is the number of states of the Turing machine. Therefore, the entire Universe is used to encode the Turing machine. The tape is not accounted for. This is somewhat of a moot point, however, since the tape of a Turing machine is (by definition) supposed to be infinite, so the real Universe couldn't accommodate a Turing machine anyway.
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As a corollary it means our universe can only make "real" Turing machines up to k states, where BusyBeaver(k) < e^10^123. If you try to make a Turing machine with k > 1, it will run out of tape for some configurations :) It looks like k is ... 5?
The first two comments are from strangers, but the last one is from me. Pretty sober to realize that Turing Machines with states less than the number of your fingers are not generally physically possible. It really puts a limit on the kinds of infinities we are supposed to imagine in math.
The Turing Machine and Halting Problem really hammer home two things:
- Computation irreducibility, and
- The hardness of differentiating between infinity and very large numbers
In fact, it seems that the busy beavers imply there's actually no difference unless you believe in some omnipotent God, because it's proven that you can't tell the difference once the numbers get sufficiently large.
We know that BB(745) = "infinity" (for integers at least). So if there's any property of numbers where finite values and infinity have different qualitative properties... the transition is between 0 and BB(745). Or we just hallucinated the properties of infinity. I tend to believe the latter is true, but maybe numbers become more surreal when they get *really* large.
Btw. Funny thing while looking up info on the subject. So this Adam Yedidia guy is a student of Scott Aaronson and was the first person to prove that BB(k) is independent of ZF for some k, and as I put his name onto Google... LOL
Just a bookmark for myself
https://www.quantamagazine.org/complexity-theorys-50-year-journey-to-the-limits-of-knowledge-20230817/
While fascinating in its own right, cryptography seemed far removed from the self-referential arguments that had first drawn Rudich and Impagliazzo into the field. But as Rudich struggled to understand why the circuit complexity approach had stalled, he began to realize that the two subjects weren’t so far apart after all. The strategy researchers had adopted in their attempts to prove P ≠ NP had a self-defeating character reminiscent of Gödel’s famous proposition “this statement is unprovable” — and cryptography could help explain why. In Russia, Razborov discovered a similar connection around the same time. These were the seeds of the natural proofs barrier.
The tension at the heart of the natural proofs barrier is that the task of distinguishing high-complexity functions from low-complexity ones is similar to the task of distinguishing true randomness from the pseudorandomness used to encrypt messages. We’d like to show that high-complexity functions are categorically different from low-complexity functions, to prove P ≠ NP. But we’d also like for pseudorandomness to be indistinguishable from randomness, to be confident in the security of cryptography. Maybe we can’t have it both ways.
Looking back, my track record at dodging hype and going all in on technologies that will change the world is still pretty good.
- Dodged the crypto one (maybe unfortunately)
- Dodged the 3d printing one (this one was really stupid TBH)
綜合各方資訊，修行最忌嘅果然都係唔夠謙遜。
無論係我自己嘅經歷、睇人哋嘅故仔、同埋理論層面，基本上都係指向呢樣嘢。
有時啲嘢係好難避免嘅，喺一個被灌輸唯物主義嘅社會，忽然俾你接觸到宇宙偉大嘅其中一小片面，現代人好容易就覺得件事不可思議，然後就覺得自己非比尋常。接觸到神聖就以為自己係耶穌呢類嘢，聽聞都成日發生。但事實就正如 Alan Watts 所講，其實所有人都係「耶穌」。又正如我所講，聖經一早提咗大家，就算係耶穌被魔鬼誘惑，佢都堅持唔濫用神力，謙虛做人，淨係用力量去救濟窮苦人家。所以如果只係接收到片面嘅神力就以為自己係耶穌然後覺得自己無敵，就肯定出事。
一開始疑似學識力量點使用，就好奇去到盡發晒啲力出去，好似係常見嘅伏位。我覺得有少少「科學精神」去試下嘢真係無可厚非，但事實上啲「魔力」又疑似真係會消牦嘅，一般人唔識發力反而冇事，但識少少唔識收斂就會出事。暫時唔知有啲咩好嘅方法避免問題 （按：我從來都唔信世界上有「貪心」呢樣嘢，「貪」字係世俗嘅嘢嚟。宇宙之大係無法想像嘅，人嘅所謂「貪念」係食唔到佢半分半毫。小器嘅係人，唔係宇宙。） 我現時覺得最接近會work嘅理論係，你只要唔係諗住同宇宙「切割」，就唔會出事。（即係愛人如己，有濟世之心之類）首先人本身唔係一個「獨立個體」而係宇宙萬物入面嘅一樣嘢。通常被歸類為「貪」嘅嘢，只不過係人將「我」同「非我」切割得太樣衰。一般嘅「損人利己」嘅操作，都係某程度上認為「我」先至係「我」，至於宇宙其他萬物，都唔關我事。但宇宙唔係有咩世俗嘅道德判斷話呢啲「貪念」係「惡」，只係呢種切割係切一半唔切一半。真正徹底嘅切割，唔係「只要我有名有利，理得你死」，而係連名利同其他世俗嘢都切晒，完全出世，不問世事。切到不問世事嗰種，反而悠然自得。而「損人利己」嗰種，係以為「錢財名利」同「世上其他人」係唔同嘅嘢嚟，但心水清嘅人就知道，根本上「錢財名利」嘅價值都係其他人賦予嘅，如果你要追求呢啲，就唔可以「理得你死」。真係唔係道德批判，而係邏輯問題。最容易理解係「名」：所謂「名」係其他人嘅仰慕。但如果「理得你死」嘅話，咁你要嘅「名」又係咩嚟？根本唔 make sense。錢都係類似。（經濟學上，我手上嘅一蚊，代表嘅係使用世界上某其他人某時間嘅權利嚟。亦理論上係代表我對世界嘅貢獻嘅價值。所以你手上每一蚊都係連接世界上每一個人嘅因果。）
理論上要避免自己「魔力」消牦得太勁，最好就係唔好自己操勞。道家講究「無為而無不為」，講嘅係順應自然，靠整個宇宙嘅力量去達成件事。至於點樣將你想要嘅嘢變成宇宙想要嘢，呢個就真係考功夫喇。理論上最簡單嘅做法係將自己想要嘅嘢變成宇宙想要嘅嘢，不過大家有自己意志嘅，要唔要開心食屎就自己諗。人生在世最大嘅「恩典」就係自由意志，呢個意志係宇宙從渾然一體之中「切割」出嚟，每個人都可以選擇「我」同「非我」之間係順應定係磨逆。理論上「天道無親」，因為宇宙係包含「我」同「非我」嘅整體，所以我可以想像「佢」會好似 Re-Zero 嘅 Echidna 咁樣用好奇嘅眼神睇下你選擇點樣掙扎。愛就係選擇吖嘛，Echidna 都係追求「愛」，佢自己全知，唯有偷窺其他人嘅選擇感受「愛」。
腦補：「愛は何故、減るのだろうか」就係因為「愛就係選擇，揀咗就冇得再揀」 :0)
諗起都唔止一次密集式撞到人
例如之前嗰晚同某某食完飯或一大班人聚會，第二日就又撞到佢咁。
幾有趣。
老豆以前都會話，啲較少類型嘅症都係平時冇，一嚟就同一日幾個咁。Hong Kali都係咁講。
唔知有啲咩特別意義，純粹係有趣嘅觀察
