Synthesis is harder than analysis

infinite_frodo•15 minutes ago

I get the point of the author about differentiation and integration. But, I did not follow completely how he connected it to analysis and synthesis. I mean, there isn't necessarily a one-to-one mapping between analysis and differentiation and synthesis and integration, right?

ajeet•about 3 hours ago

I loved reading this article. It was reasonably short to not make the reader lose interest. It jumped around in different domains to make a core point at the end about SREs managing complex systems. This gets even more difficult with the rate of change each of those systems has with coding agents. I don't know if I agree with the terms "synthesis" and "analysis" as the equivalent of global and local respectively, but it was a great read.

dreamcompiler•about 3 hours ago

> And it turns out that it’s quite straightforward to calculate a derivative, no matter what type of function it is.

I get the author's point but this is not completely true; there exist functions that are not differentiable at certain places (e.g. ideal square waves) and others that are not differentiable anywhere (e.g. Weierstrass functions).

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

jonlong•26 minutes ago

It's important to know that (in the usual setting of analysis) not every function is everywhere (or even anywhere) differentiable, but this is more orthogonal to the author's point than opposed to it. A square wave is piecewise differentiable and you can compute a piecewise derivative. The Weierstrass function is defined by an infinite series, and you can compute its derivative term-by-term by the usual rules and check that the result does not converge; it is indeed straightforward to calculate its nonexistent derivative, and this is what Weierstrass did!

In general, to even ask what it means to compute a derivative we need to specify some input language which describes functions in finite terms; we are necessarily in the world of constructions rather than (say) arbitrary set-theoretical maps between infinite sets. With this in mind, the claim that differentiation is always a straightforward computation is a strong one.

dcrazy•about 3 hours ago

> (Note: I asked AI for the integral of the Gaussian, I hope it got it right!)

It seems like malpractice to not even check this.

tikhonj•about 2 hours ago

It's an illustration for a blog post on a largely different subject, it really doesn't matter.

Who would be looking up the integral of one of the most common functions in applied math in a random philosophical article aimed mostly at SREs?

taneq•about 2 hours ago

I don’t think the word applies to a blog post which its self-described as “ramblings”. The formula’s there to look scary and illustrate a point, nobody’s using it to integrate a Gaussian.

jdw64•about 2 hours ago

The reason synthesis expertise is not easily recognized as expertise might be because it's hard to evaluate when moving to another system.

Analysis expertise is about knowing the limitations of specific languages, libraries, and frameworks, and this is easy to recognize and evaluate. But synthesis expertise, by its nature, is about 'combining systems within a specific company.' When you change jobs, it's hard to apply that combination to a completely different system.

For example, even if you know why a company's API design and structure were shaped the way they are, that doesn't necessarily mean you can use that knowledge directly at your next company. Maybe that's why.

taneq•about 2 hours ago

> However, when someone says “calculus” without modification […] there’s no ambiguity about which calculus they are referring to

Might be differentiation and integration, might be dental plaque. ;)

apsurd•about 3 hours ago

Yes, this is documented in Bloom's Taxonomy for learning/education. Creating is the highest level of understanding.

    Remember – Recall facts, definitions, formulas (memorization).
    Understand – Explain ideas in your own words.
    Apply – Use knowledge to solve problems or perform tasks.
    Analyze – Break information into parts and identify relationships.
    Evaluate – Judge, critique, or justify decisions.
    Create – Synthesize ideas to produce something new.

Synthesis is harder than analysis

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