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Comment by kingkongjaffa | Hacker News Reader

Agreed, these kind of titles are very silly.

FTs are actually very reasonable, in the sense that they are a easy to reason about conceptually and in practice.

There's another title referenced in that link which is equally asinine: "Eugene Wigner's original discussion, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". "

Like, wtf?

Mathematics is the language of science, science would not compound or be explainable, communicable, or model-able in code without mathematics.

It's actually both plainly obvious for mathematics then to be extremely effective (which it is) and also be evidently reasonable as to why, ergo it is not unreasonably effective.

Also the slides are just FTs 101 the same material as in any basic course.

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Hi, original presenter here :) The beginning is FTs 101. The end gets more application-centric around OFDM and is why it feels 'unreasonably effective' to me. If it feels obvious, there's a couple of slides at the end that are food for thought jumping off points. And if that's obvious to you too, let's collab on building an open source LTE modem!

If one wants to contribute to an open-source LTE modem, the best place to start may be OpenLTE: https://en.wikipedia.org/wiki/OpenLTE The core of any LTE modem is software, even if it is written for DSPs or other low-level software.

> FTs are actually very reasonable, in the sense that they are a easy to reason about conceptually and in practice.

ok but it's not the FTs that are unreasonable, it's the effectiveness

I think we all understand at this point that "unreasonable effectiveness" just means "surprisingly useful in ways we might not have immediately considered"

The HN audience is filled with the world's densest collection of literalists and nitpickers: software engineers.

Metaphorical language compels them to microrebuttals.

I find it hard to parse the middle of your post. Are you saying Wigner's article, which is what all the "unreasonable effectiveness" titles reference, is silly?

If that is what you are saying I suggest that you actually go back and read it. Or at least the Wiki article:

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

By means of contrast: I think it's clear that mathematics is, for example, not unreasonably effective in psychology. It's necessary and useful and effective at doing what it does, but not surprisingly so. Yet in the natural sciences it often has been. This is not a statement about mathematics but about the world.

(As Wittgenstein put it some decades earlier: "So too the fact that it can be described by Newtonian mechanics asserts nothing about the world; but this asserts something, namely, that it can be described in that particular way in which as a matter of fact it is described. The fact, too, that it can be described more simply by one system of mechanics than by another says something about the world.")

Yeah it's silly, I don't mean it in any mean spirited way.

> Wigner's first example is the law of gravitation formulated by Isaac Newton. Originally used to model freely falling bodies on the surface of the Earth, this law was extended based on what Wigner terms "very scanty observations"[3] to describe the motion of the planets, where it "has proved accurate beyond all reasonable expectations."

So despite 'very scant observations' they yielded a very effective model. Okay fine. But deciding they should be 'unreasonably' so is just a pithy turn of phrase.

That mathematics can model science so well, is reductive and reduces to the core philosophy of mathematics question of whether it is invented or discovered. https://royalinstitutephilosophy.org/article/mathematics-dis...

Something can be effective, and can be unreasonably so if it's somehow unexpected, but I basically disagree that FTs or mathematics in general are unreasonably so since we have so much prior information to expect that these techniques actually are effective, almost obviously so.

I am not discussing the FT case. But as regards Wigner's article, the core thing he points out is that while we are used to the effectiveness of maths, centuries after Newton, there in fact is not any prior grounds to expect this effectiveness.

And no, this is unrelated to whether math is invented or discovered. If anything this is related to the extreme success of reductionism in physics.

As a general point of reflection: If an influential article by a smart person seems silly to you, it's good practice to entertain the question if you missed something, and to ask what others are seeing in it that you're missing.

> Mathematics is the language of science

So, biology and medicine are not sciences? Or are only sciences to the extent they can be mathematically described?

The scientific method and models are much more than math. Equating the reality with the math has let to myriad misconceptions, like vanishing cats.

And silly is good for a title -- descriptive and enticing -- to serve the purpose of eliciting the attention without which the content would be pointless.

They are still capable of being described with math, we are just not capable of doing the math, or probably better put is there is a diminishing return of doing the formalisation of those systems as our cognitive abilities are limited and couldn't reason about those models. It leaves them using very approximate models based on human language descriptions that can be reasoned about.

Which means, the language of some fields can’t be math.

However, I don’t think the original presenter was asserting those fields aren’t science, that’s an unreasonable interpretation. More so , ideally they would be use math as it is a language that would help prevent the silly argument “so, Y is not X?, or is Y only X provided Y is in the subset of X that excludes Z? “

(Even in Engineering, we hit this cognitive limit, and all sorts of silliness emerges about why things are or are not formalised)

It is likewise unreasonable to look down on any kind of world model from the past. Remember that you, in 2026, are benefitting from millions of aggregate improvements to a world model that you've absorbed passively through participation in society, and not through original thought. You have a different vantage point on many things as a result of the shoulders of giants you get to stand on.

It is pretty funny to flippantly call an influential paper by someone who received a Nobel Prize in Physics 'asinine'.

I mean... this one's actually a pretty good paper, but we also had Linus Pauling pontificate on Vitamin C, so maybe we should cool it with the appeals to Nobel authority alone.

He did have a very long life, so there's that.

It's not easy to separate cause and effect from direct and strong correlations that we experience.

The job of a scientist is not to give up on a hunch with a flippant "correlation is not causation" but pursue such hunches to prove it this way or that (that is, prove it or disprove it). It's human to lean a certain way about what could be true.

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