MIT's Williams Attacks SETH to Drive Algorithmic Breakthroughs

Ryan Peterman

Assuming the Strong Exponential Time Hypothesis is false forces researchers away from standard methods, producing mathematical breakthroughs from failed refutations regardless of whether the conjecture is ultimately true.

AI-assisted summary of MIT Professor: Why Contrarian Thinking Improves Your Thoughts | Ryan Williams — original source. Check the original for full context.

Source published: 2026-10-27

Key ideas

The Strong Exponential Time Hypothesis (SETH) represents a severe strengthening of P vs. NP, conjecturing that general CNF-SAT cannot be solved in (2 - ε)^n time for any constant ε > 0. (0:00)
MIT Professor Ryan Williams remains on record as skeptical of SETH, motivated by known algorithms beating 2^n on related NP-complete problems like Subset Sum and 3-SAT. (1:58)
Williams treats disbelieving SETH as an operational forcing function, using failed algorithmic attacks to discover mathematical structures that resolve other major open problems in complexity theory. (3:44)

Detailed notes

## Background Published by Ryan Peterman on YouTube on October 27, 2026, this video features an interview clip with MIT professor and Gödel Prize winner Ryan Williams, exploring theoretical computer science and algorithmic thinking following a broader discussion on interview problems.

## TL;DR In this discussion, theoretical computer scientist Ryan Williams breaks down the Strong Exponential Time Hypothesis (SETH), which posits that general CNF-SAT cannot be solved faster than brute-force search around 2^n time. Williams shares his longstanding skepticism toward the conjecture, noting that known faster-than-brute-force algorithms for 3-SAT and Subset Sum suggested that general SAT might also be beatable. Although his direct attempts to refute SETH repeatedly failed in catastrophic ways, examining the mechanisms behind those failures yielded breakthrough techniques that resolved other major open problems. Ultimately, Williams argues that assuming SETH is false serves as a vital operational forcing function that propels his research toward non-obvious ideas.

## Atmosphere & style The conversation carries an intellectually playful, reflective, and candid tone. Host Ryan Peterman guides the exchange with targeted theoretical prompts, allowing Williams to speak with self-deprecating humor about his age and his 'catastrophic' failed attempts at breaking complexity barriers. Watching it feels like listening to a world-class mathematician demystify high-level research, transforming rigid computational boundaries into an engaging philosophical lesson on the creative value of contrarian failure.

## Bulletin - [00:00](https://www.youtube.com/watch?v=LRVprar87W0&t=0s) The Strong Exponential Time Hypothesis (SETH) represents a severe strengthening of P vs. NP, conjecturing that general CNF-SAT cannot be solved in (2 - ε)^n time for any constant ε > 0. - [01:58](https://www.youtube.com/watch?v=LRVprar87W0&t=118s) MIT Professor Ryan Williams remains on record as skeptical of SETH, motivated by known algorithms beating 2^n on related NP-complete problems like Subset Sum and 3-SAT. - [03:44](https://www.youtube.com/watch?v=LRVprar87W0&t=224s) Williams treats disbelieving SETH as an operational forcing function, using failed algorithmic attacks to discover mathematical structures that resolve other major open problems in complexity theory.

## Key takeaways - [00:00](https://www.youtube.com/watch?v=LRVprar87W0&t=0s) SETH strengthens the P vs. NP question by claiming general SAT is not just super-polynomial, but essentially requires brute-force 2^n time in the worst case. - [00:35](https://www.youtube.com/watch?v=LRVprar87W0&t=35s) The formal formulation of SETH is defined over k-SAT as clause length k grows arbitrarily large. - [01:00](https://www.youtube.com/watch?v=LRVprar87W0&t=60s) A stark divide exists between theory and practice: modern SAT solvers efficiently handle industrial software and hardware verification, yet theoretical worst-case bounds remain bounded near 2^n. - [02:08](https://www.youtube.com/watch?v=LRVprar87W0&t=128s) Williams began attempting to beat the 2^n bound for general CNF-SAT during his undergraduate and early graduate school years, before SETH was formally named. - [02:34](https://www.youtube.com/watch?v=LRVprar87W0&t=154s) Non-trivial algorithms already beat naive exhaustive search for other NP-complete problems, such as Subset Sum. - [02:44](https://www.youtube.com/watch?v=LRVprar87W0&t=164s) Restricting clause length to three literals in 3-SAT allows algorithms to run strictly faster than 2^n, prompting Williams to question why general SAT should have a rigid 2^n lower bound. - [03:44](https://www.youtube.com/watch?v=LRVprar87W0&t=224s) Williams's repeated attempts to refute SETH routinely failed in catastrophic and absurd ways on the target SAT problem. - [04:00](https://www.youtube.com/watch?v=LRVprar87W0&t=240s) By deeply analyzing the mechanics of catastrophic failures, Williams repurposed broken techniques to solve entirely different open problems in theoretical computer science. - [04:18](https://www.youtube.com/watch?v=LRVprar87W0&t=258s) Williams views the actual truth value of SETH as secondary to the generative value of believing it to be false. - [04:32](https://www.youtube.com/watch?v=LRVprar87W0&t=272s) Assuming SETH is false acts as a cognitive forcing function, instantly ruling out conventional algorithmic ideas and directing thought toward non-obvious paradigms. - [05:12](https://www.youtube.com/watch?v=LRVprar87W0&t=312s) Contrarian belief can serve as an exceptionally productive research heuristic even in the absence of an ultimate proof or refutation.

## Detailed walkthrough ### [00:00](https://www.youtube.com/watch?v=LRVprar87W0&t=0s) Understanding the Strong Exponential Time Hypothesis (SETH)

Ryan Peterman introduces the topic by asking Ryan Williams to explain the Strong Exponential Time Hypothesis (SETH) and why it holds such significance in theoretical computer science. Williams frames the concept by contrasting it directly with the field's most famous open problem: “Strong ETH is like a severe strengthening of the P versus NP question.” While $P \text{ vs } NP$ fundamentally asks whether the Boolean satisfiability problem (SAT) can be solved in polynomial time or not, the Strong Exponential Time Hypothesis makes a far more drastic assertion. SETH posits that general SAT cannot be solved significantly faster than brute-force search—specifically, that there is no algorithm running in $O(1.999^n)$ time, or $(2 - \varepsilon)^n$ for any constant $\varepsilon > 0$, no matter how many nines one appends after the decimal.

Williams explains that a completely precise formulation of the hypothesis is stated in terms of the $k$-SAT problem, where one considers Boolean formulas in conjunctive normal form with clauses of length $k$ as $k$ grows arbitrarily large. In practical domains, SAT is ubiquitous; Williams points out that modern SAT solvers work remarkably well on real-world inputs and function as an essential engine for industrial software and hardware verification. However, theoretical computer science focuses on worst-case complexity, and in that worst-case setting, nobody knows how to beat $2^n$ search time in general. Contrasting it once more with standard complexity bounds, Williams emphasizes the sheer extremity of the conjecture: “It says that no no no no, it's not super polynomial. It's actually darn near 2 the n time that you need.”

- **P vs. NP baseline:** Asks whether SAT has a polynomial-time algorithm ($P = NP$) or requires super-polynomial time ($P \neq NP$). - **SETH assertion:** In the worst case, general CNF-SAT cannot be solved in $(2 - \varepsilon)^n$ time; for any fixed string of decimals like $1.9999\dots$, no algorithm exists that scales bounded away from $2^n$. - **Real-world vs. theoretical divide:** Despite worst-case exponential hardness, specialized heuristics solve industrial SAT instances efficiently every day for verification and automated reasoning.

---

[01:58](https://www.youtube.com/watch?v=LRVprar87W0&t=118s) Doubting SETH: Early Intuitions and the 3-SAT Contrast

When Peterman asks whether he personally believes the hypothesis to be true, Williams admits his skepticism: “I think I'm on the record as not believing this hypothesis.” He recounts that his fascination with beating $2^n$ began long before the conjecture even had its current name, thinking back to his days as an undergraduate and the early stages of graduate school—quipping that this timeline “shows how old I am.” At that time, he was actively trying to find faster algorithms for general CNF-SAT because standard intuition from other NP-complete problems suggested room for improvement.

Williams notes that several canonical NP-complete problems had already yielded non-trivial algorithms that beat naive exhaustive search, such as Subset Sum. Furthermore, restricted variations of satisfiability itself were already known to be solvable strictly faster than $2^n$ time. In 3-SAT, where each clause is restricted to a disjunction of at most three literals (variables or their negations) conjoined together, specialized algorithms successfully break the $2^n$ barrier. Williams reasoned that if 3-SAT and other related NP-complete problems allowed for faster-than-brute-force upper bounds, there was no foundational reason to assume general SAT was burdened with such a rigid lower bound.

```mermaid flowchart TD accTitle: Williams's Skepticism Toward SETH accDescr: Flowchart contrasting known upper bounds in NP-complete problems against the assumption of SETH hardness. subgraph KnownUpperBounds["Known Faster Algorithms (< 2^n)"] A["Subset Sum"] B["3-SAT (< 2^n algorithms exist)"] end subgraph SETHConjecture["SETH Lower Bound Claim"] C["General CNF-SAT requires ~2^n"] end KnownUpperBounds -.->|"Contradicts natural intuition"| D["Williams's Initial Skepticism:<br/>'Why should general SAT be so special?'"] SETHConjecture -.-> D ```

---

[03:44](https://www.youtube.com/watch?v=LRVprar87W0&t=224s) The Productive Power of Catastrophic Failure and Contrarian Belief

Williams recounts how his attempts to disprove SETH shaped his entire research methodology. Over the years, he launched numerous attacks aimed at refuting the hypothesis by constructing faster algorithms. Invariably, these attempts collapsed: they would fail in what he describes as “some completely catastrophic and ridiculous way” that left zero hope of solving the original SAT problem. Rather than abandoning the wreckage, Williams developed the habit of staring deeply into the failed mechanics, asking what peculiar phenomenon was actually occurring beneath the surface. By pivoting and repurposing the salvageable mathematical structures from those failures, he repeatedly discovered that the broken techniques could solve entirely different, previously open problems.

Through this cycle, Williams arrived at an unconventional philosophy: the objective truth or falsity of SETH is practically secondary to the generative power of disbelieving it. He explains that assuming the hypothesis is false serves as a powerful operational forcing function: “And so, after a while, I realized that the truth value of strong ETH to me is almost irrelevant. Like because if I believe that it's false, then I get good ideas.” Because all obvious, conventional techniques are already proven incapable of beating $2^n$, setting out to break the barrier forces him to discard standard approaches immediately and steer his thoughts in non-obvious directions. Williams reflects that even without an ultimate refutation in hand, contrarian optimism remains his most potent research engine: “I mean, even even though I still haven't refuted it or whatever, like it's very useful for me to believe that it's false. Like, operationally.”

```mermaid flowchart LR accTitle: Williams's Contrarian Research Heuristic accDescr: Diagram illustrating how assuming SETH is false leads to failures that unlock breakthroughs in other problems. subgraph Heuristic["Contrarian Hypothesis"] A["Assume SETH is False"] --> B["Force Brain Away from<br/>Standard Algorithmic Ideas"] end subgraph Execution["Attack & Pivot"] B --> C["Attack CNF-SAT (< 2^n)"] C --> D["Catastrophic Failure on SAT"] D --> E["Stare at Mechanics of Failure"] E --> F["Solve Other Major Open Problems"] end ```

- **Embracing failure:** Unsuccessful refutations of SETH yielded mathematical insights that solved other foundational problems across computational complexity. - **Cognitive forcing function:** Assuming SETH is false eliminates ordinary proof paths that are known dead ends, compelling the researcher to invent alternative paradigms. - **Operational utility:** A hypothesis can function as a productive intellectual tool regardless of whether it is ultimately proven true or false.

## Notable quotes > [03:44](https://www.youtube.com/watch?v=LRVprar87W0&t=224s) I realized that the truth value of strong ETH to me is almost irrelevant. Like because if I believe that it's false, then I get good ideas. — Ryan Williams

> [00:00](https://www.youtube.com/watch?v=LRVprar87W0&t=0s) Strong ETH is like a severe strengthening of the P versus NP question. — Ryan Williams

## Mentioned Ryan Williams, Ryan Peterman, Strong Exponential Time Hypothesis (SETH), P vs NP, Boolean satisfiability problem (SAT), 3-SAT, k-SAT, Subset Sum, Gödel Prize, Massachusetts Institute of Technology (MIT)

## Video description Ryan Williams is a professor at MIT and the winner of the Gödel Prize in theoretical computer science. I interviewed him all about his work starting by asking him a popular Leetcode question (3 SUM).

Watch the full conversation: https://www.youtube.com/watch?v=AaK1SL2i_4Y

[Source](https://www.youtube.com/watch?v=LRVprar87W0)

中文简报

麻省理工学院Williams挑战SETH以推动算法突破假定强指数时间假设不成立会迫使研究人员脱离常规方法；无论该猜想最终是否成立，推翻尝试的失败都能催生数学上的突破。在这场讨论中，理论计算机科学家Ryan Williams剖析了强指数时间假设（SETH），该假设认为通用CNF-SAT无法在快于约2^n时间的暴力搜索下解决。Williams分享了他对该猜想长期持有的怀疑态度，指出已知在3-SAT和子集和问题上存在优于暴力搜索的算法，这表明通用SAT或许同样可以被超越。尽管他直接推翻SETH的尝试多次遭遇彻底失败，但深入分析这些失败背后的机制却催生出了突破性技术，并解决了其他重大的未解难题。最终，Williams认为，假定SETH不成立充当了一种关键的实践推动力，促使他的研究走向非常规的思路。强指数时间假设（SETH）是对P与NP问题的严格强化，猜想对于任何常数ε > 0，通用CNF-SAT都无法在(2 - ε)^n时间内得到解决。 (0:00) 麻省理工学院教授Ryan Williams公开对SETH持怀疑态度，其依据是已知算法在子集和及3-SAT等相关NP完全问题上的运行速度已突破2^n。 (1:58) Williams将对SETH的怀疑视为一种实践推动力，利用算法攻击的失败去发现数学结构，进而解决了复杂度理论中的其他重大未解难题。 (3:44)

Reading summary

Theoretical computer scientist Ryan Williams argues that deliberately disbelieving the Strong Exponential Time Hypothesis serves as a generative operational tool, forcing researchers away from conventional dead ends to uncover unexpected mathematical breakthroughs. The Rigidity of the Strong Exponential Time Hypothesis (0:00) The Strong Exponential Time Hypothesis (SETH) represents a severe strengthening of the classic P versus NP question. While P versus NP asks whether the Boolean satisfiability problem (SAT) can be solved in polynomial time or requires super-polynomial time, SETH asserts that general CNF-SAT cannot be solved significantly faster than exhaustive brute-force search. Specifically, the hypothesis posits that no algorithm can solve general SAT in O((2 - ε)^n) time for any constant ε > 0, ruling out upper bounds such as O(1.999^n). Williams highlights a sharp divide between industrial practice and complexity theory. Modern SAT solvers efficiently resolve real-world instances every day, serving as core engines for hardware and software verification. However, theoretical computer science measures worst-case complexity, and in that worst-case regime, general SAT algorithms consistently fail to beat the 2^n search barrier as clause lengths grow arbitrarily large in k-SAT formulations. Precedents Challenging the 2^n Barrier (1:58) Williams is publicly on record as a skeptic of SETH, tracing his doubt to his undergraduate and early graduate studies before the conjecture received its formal name. His skepticism arose from comparing general SAT to other canonical NP-complete problems that had already yielded algorithms beating naive exhaustive search, such as Subset Sum. Furthermore, restricted variations of satisfiability had already breached the brute-force threshold. In 3-SAT, where clauses are restricted to at most three literals, specialized algorithms strictly break the 2^n time barrier. Williams reasoned that if 3-SAT and related NP-complete problems admit faster-than-brute-force upper bounds, theoretical computer science provides no foundational rationale for assuming general CNF-SAT is bound to an inflexible 2^n lower bound. Catastrophic Failures as Generative Research Tools (3:44) Williams's attempts to disprove SETH by constructing faster algorithms repeatedly resulted in what he terms catastrophic failures that offered zero hope of solving the original SAT problem. Rather than discarding the failed attempts, Williams closely analyzed the mechanics of why the algorithms broke down. By isolating and repurposing the salvageable mathematical structures from those breakdowns, he discovered techniques that resolved entirely different, previously open problems in computational complexity. Through this iterative process, Williams concluded that the objective truth value of SETH is secondary to the operational value of disbelieving it. Because conventional techniques are mathematically guaranteed to fail at beating 2^n, adopting the contrarian assumption that SETH is false acts as an intellectual forcing function. It requires the researcher to immediately discard conventional approaches and explore non-obvious paradigms that yield productive ideas. Although Williams has not formally refuted SETH, he maintains that contrarian optimism functions as his most potent research engine. The approach illustrates how adopting an unproven contrarian premise can yield foundational discoveries, even when the original hypothesis remains unresolved.

精炼阅读摘要

MIT理论计算机科学家Ryan Williams指出，在计算复杂度研究中，坚持认定强指数时间假说（SETH）为假这一逆向立场，能够成为极具生产力的思维工具；通过直面算法攻关中的灾难性失败并提取其数学机制，往往能催生出解决其他开放难题的突破性成果。 SETH假说与最坏情况复杂度界限 (0:00) Williams解释称，强指数时间假说（SETH）可以被视为经典P与NP问题（P vs NP）的激进化延伸。P与NP问题探讨布尔可满足性问题（SAT）是否存在多项式时间解法，而SETH则给出了更严苛的猜想：在最坏情况下，一般形式的合取范式可满足性问题（CNF-SAT）无法在显著快于暴力搜索的时间内求解，即不存在运行时间达到O(1.999^n)或(2 - ε)^n（其中ε > 0为常数）的算法，无论在底数的小数点后添加多少个9，都无法摆脱接近2^n的时间界限。该假说在严格表述中基于子句长度k任意增大的k-SAT问题展开。在实际应用领域，现代SAT求解器已被广泛用于软件与硬件的工业级自动化验证，并在实际输入上表现出极高的效率。然而，Williams强调理论计算机科学关注的是最坏情况复杂度，而在最坏情境的理论层面，学界至今仍无人知晓如何在一般情况下突破2^n搜索时间的极限。质疑SETH的理论直觉与3-SAT反例 (1:58) Williams明确表示自己公开持怀疑SETH的立场，并透露这一研究兴趣始于其本科及研究生早期阶段。他的怀疑直觉源于其他NP完全问题的已知算法进展：例如子集和问题（Subset Sum）等经典难题早已被证明存在优于朴素穷举搜索的非平凡算法。此外，在可满足性问题自身的受限形式中，针对每个子句至多包含三个文字的3-SAT问题，理论上已经存在打破2^n时间界限的专用算法。Williams据此推论，既然3-SAT及其他相关NP完全问题均能实现超越暴力搜索的时间上界，便没有充足的理论理由假定一般CNF-SAT必然受制于如此僵硬的2^n计算下界。灾难性失败与逆向思维的生产力 (3:44) 为了尝试证伪SETH，Williams多年来多次试图构建超越2^n限制的更快速算法，但这些尝试均以他所形容的“灾难性且荒谬的方式”崩溃，无法直接攻克最初的SAT难题。然而，他并未直接抛弃这些失败尝试，而是深入剖析算法崩溃的底层数学机制，并通过重新利用这些失败残留的结构，多次成功解决了理论计算机科学中其他长期未决的重要开放问题。这一过程使Williams确立了一种非常规的研究哲学：SETH在客观上的真假对其工作而言几乎是次要的，关键在于“认定其为假”这一信念所产生的启发价值。由于所有常规技术均已被证实无法超越2^n时间屏障，确信该假说为假成为一种强制性的认知驱动力，迫使研究者立即舍弃显而易见的研究死角并探索非传统方向。Williams总结认为，即便目前尚未真正证伪SETH，这种逆向的乐观主义在操作层面依然是他最强大的研究引擎。尽管Williams尚未在数学上推翻SETH，但他认为将假说作为方法论工具的操作效用远超对其真伪的单纯评判；在常规方法均告失效的理论领域，逆向信念能有效迫使思维脱离定势，在直面极端失败的过程中拓展认知边界。

Source quotes

[3:44] Ryan Williams: I realized that the truth value of strong ETH to me is almost irrelevant. Like because if I believe that it's false, then I get good ideas. [0:00] Ryan Williams: Strong ETH is like a severe strengthening of the P versus NP question.

Original transcript

[0:00] strong exponential time hypothesis. I [0:02] see it, you know, SETH. [0:05] Um, could you explain that and its [0:07] significance? [0:08] >> Strong ETH is like a severe [0:10] strengthening [0:12] of the P versus NP question. [0:14] So, [0:16] P versus NP is um asking whether the SAT [0:21] problem um [0:23] has a polynomial time algorithm or not. [0:27] Right? And strong ETH [0:30] is basically saying that [0:33] for the SAT problem uh you cannot solve [0:37] it faster [0:39] than much faster than 2 the n. So, [0:42] there's no 1.999 [0:45] to the n time algorithm. [0:47] For every string of nines, there is no [0:50] 1.9999 to the n time algorithm. [0:54] Um to say the hypothesis totally [0:57] precisely, it has to do with the K-SAT [0:59] problem. And you're looking at [1:02] clauses of [1:04] length K for arbitrary K, but [1:08] um [1:09] those details don't matter so much. It's [1:11] a canonical NP-complete problem. SAT is [1:15] solved all the time in practice. It's [1:19] extremely useful for a verification [1:22] nowadays. It's an It's an engine [1:24] for verification. Um so, it can be [1:27] solved fairly well in practice. [1:30] However, in the worst case, we still [1:33] don't know how to solve it uh [1:35] significantly faster than 2 the n. [1:38] So, the hypothesis that it needs, say, [1:41] 1.99999 [1:43] to the n time for all strings of nines [1:45] is a very strong [1:48] exponential time hypothesis. It was [1:50] stronger than P different from NP. It [1:52] says that no no no no, it's not super [1:54] polynomial. It's actually darn near 2 [1:56] the n time that you need. [1:58] >> Right. And so, do you think that [2:01] hypothesis is true and you know, why or [2:04] why not? [2:05] >> I think I'm on the record as not [2:07] believing this hypothesis. Yeah. Um [2:11] Yeah, why don't I believe this [2:13] hypothesis? Um [2:16] Well, I started thinking about this [2:17] hypothesis [2:19] maybe already as an [2:22] undergrad, but certainly starting [2:25] um in grad school. [2:27] Like early in grad school I was thinking [2:28] about this. So, before it was even [2:30] called strong ETH, I guess that shows [2:33] how old I am. Uh I was trying to think [2:35] about how to solve [2:38] what this so-called CNF SAT problem [2:40] faster than 2 to the n. [2:42] And [2:43] well, at the time [2:45] there were a number of other NP-complete [2:48] problems that had faster algorithms like [2:51] subset sum. [2:53] So, I thought, well, there's not I mean, [2:56] what's so special about SAT? Like, if [2:58] all these other problems have faster [3:00] algorithms um why not SAT as well? [3:04] Like if you restrict to the 3-SAT [3:07] problem [3:09] like So, this is where [3:11] you have an and of these clauses. Each [3:14] clause has like is an or of three uh [3:18] variables. Some of the variables may be [3:21] negated. [3:22] You want to know if there's a way to set [3:23] all the variables to make all the [3:25] clauses simultaneously true. Um there is [3:28] a faster algorithm for that. [3:30] Um but this is a more general version of [3:32] SAT. Um [3:34] So, at first I just thought, well, [3:36] there's no good reason to think in a [3:38] lower bound these other related problems [3:40] have upper bounds. [3:42] So, why not? [3:43] But then [3:44] um over time I would have different [3:47] attacks [3:49] on strong ETH. Like trying to refute it. [3:51] Always trying to refute it in different [3:54] ways, these attacks would fail. [3:57] And some completely catastrophic and [4:02] ridiculous way, like um they would like [4:06] have no chance of [4:08] actually solving the original problem. [4:10] But by sort of staring at my failure and [4:14] trying to think, well, there's something [4:15] interesting happening here. What can I [4:17] do with this? Like there's something [4:20] interesting. Yeah, it doesn't refute uh [4:23] the strong ETH thing. [4:25] What does it do? And so, by trying to [4:28] pivot and figure out, okay, what can I [4:30] do with my failure, [4:32] I was able to solve a like a variety of [4:35] other problems instead. [4:37] And so, after a while, I realized that [4:40] the truth value [4:41] of strong ETH to me [4:44] is almost irrelevant. Like because if I [4:46] believe that it's false, then I get good [4:49] ideas. [4:51] I get I get good ideas. Like [4:53] and [4:54] so, by trying to think about, okay, what [4:58] would an algorithm that breaks through [5:01] the end look like? What could it look [5:03] like? [5:04] I I sort of force myself to think in a [5:07] different way. Like I I I I have to like [5:10] discard [5:11] other natural algorithmic possibilities [5:13] because we know they they won't work. [5:16] Um [5:17] and I have to think in a in a different [5:20] direction. And so, [5:22] because it kind of like sends my brain [5:25] in a different direction, sends me [5:27] thinking a different way, it's very [5:29] useful for research. [5:31] You know, you go [5:32] I mean, even even though I still haven't [5:34] refuted it or whatever, like it's very [5:37] useful for me to believe that it's [5:39] false. Like, operationally.