# projection Published articles for projection. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## History of SpaceX: Synthesis, the Independence Assumption, and Projection through 2050 DevFeed: [History of SpaceX: Synthesis, the Independence Assumption, and Projection through 2050]() Original publisher: [Read original article]() Author: Brendan Sechter Published: 2026-08-05T09:00:00Z Content type: opinion Language: en Sources: [Brendan A R Sechter's Development Blog]() Topics: [Framework]() Tags: [aerospace](), [analysis](), [business](), [framework](), [history](), [open-questions](), [projection]() ### AI overview This concluding article in a History of SpaceX series retrospectively assesses the series' framework, argues that its supposedly separable conditions are coupled, and examines how that independence assumption affects assessment. It also projects the analysis to 2050 under stated assumptions, ranks failure modes, and identifies unresolved questions. ### Source excerpt This article closes the History of SpaceX series. It has three tasks. The first is retrospective, restating the seven forcing-function conditions and the three capital-formation legs that the series opener introduced and that the intervening ten articles developed, and assessing what each turned out to establish. The second is critical, and it is the article's principal contribution. Across three independent articles the series encountered the same structural surprise, namely that conditions the framework treats as separable are in fact coupled, and the closing article argues that the coupling is general and not incidental and that the framework's independence assumption biases the assessment in opposite directions depending on the state of the world. The third is projective, extending the analysis to 2050 under explicitly stated assumptions and with the failure modes ranked, not merely listed. The article treats the alternative contemporary configurations that the commentary offers as templates, comprising the defense-technology venture, the failed-governance case, the intelligence-anchor case, and the patient-single-funder case, and the deep historical precedents comprising the industrial consolidation, the corporate research laboratory, the endowed foundation, the mass-production firm, and the early aircraft manufacturers. The article closes with the load-bearing open questions the series as a whole leaves unresolved, which are more numerous than any single article's closing section suggested. The Synthesis Problem The mapping problem for a closing article differs from that of the eleven that precede it. Those articles each asked what happened along one dimension. This one asks whether the dimensions were the right ones, whether the framework built from them holds together, and what it predicts. The series advanced a thesis, which the series opener states as the singular-conjunction claim. The claim is that a particular venture is the only modern case satisfying ## The Inner Product as a Decision Rule DevFeed: [The Inner Product as a Decision Rule]() Original publisher: [Read original article]() Published: 2017-05-22T08:00:00Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [math](), [Code]() Tags: [arithmetic](), [inner-product](), [javascript](), [linear-algebra](), [machine-learning](), [math](), [mathematics](), [programming](), [projection](), [support-vector-machines](), [vectors]() ### AI overview This article explains how the standard inner product, or dot product, acts as a geometric decision rule. It shows how the sign of the product determines which side of a line through the origin a vector lies on, while zero indicates that the vector lies on the line. The explanation connects this behavior to vector projection. ### Source excerpt The standard inner product of two vectors has some nice geometric properties. Given two vectors $ x, y \in \mathbb{R}^n$, where by $ x_i$ I mean the $ i$-th coordinate of $ x$, the standard inner product (which I will interchangeably call the dot product) is defined by the formula $$\displaystyle \langle x, y \rangle = x_1 y_1 + \dots + x_n y_n$$ This formula, simple as it is, produces a lot of interesting geometry. ## The Codes of Solomon, Reed, and Muller DevFeed: [The Codes of Solomon, Reed, and Muller]() Original publisher: [Read original article]() Published: 2015-03-23T09:00:00Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Code](), [Decoding]() Tags: [code](), [coding-theory](), [decoding](), [hamming-code](), [information-theory](), [linear-codes](), [projection](), [reed-muller-code](), [reed-solomon-code]() ### AI overview This article introduces Reed-Solomon codes, explains the Singleton bound for codes with parameters (n,k,d)q, proves the bound using a projection map, and relates codes that meet the bound to maximum distance separable codes. It also places Reed-Muller codes in the broader discussion. ### Source excerpt Last time we defined the Hamming code. We also saw that it meets the Hamming bound, which is a measure of how densely a code can be packed inside an ambient space and still maintain a given distance. This time we'll define the Reed-Solomon code which optimizes a different bound called the Singleton bound, and then generalize them to a larger class of codes called Reed-Muller codes. In future posts we'll consider algorithmic issues behind decoding the codes, for now we just care about their existence and optimality properties.