Comment by epolanski | Hacker News Reader

Comment by epolanski | Hacker News Reader

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Problem is as always greed for fame, power and money.

Labs and researchers are given funds based on "impact".

As we all know, when a metric becomes the goal, the metric gets gamified.

This is very hard to fix.

Gonna give you an example. As soon as you move in any direction in science you're entering a niche. Pretty much everything is its own niche where there's a limited number of people really able to review your paper.

No, there's not thousands of experts dedicating their life to helicoidal peptides interactions with metal layers. It's an extremely small number of people. They all know each other and are gonna review each other's papers regularly.

Solar-powered water splitting to produce hydrogen and oxygen? Again, extremely small club.

Perovskite? Graetzel solar cells? Bigger club, but still, at the end of the day the relevant luminaries are a handful again.

You think it's much different for quaternions or advanced complex numbers analysis?

And those small clubs set the rules and standards, and there is really not much way to have oversight on those small clubs.

Plenty of terrible science is published every day, I can confidently say 90 to 95% of experiments in Physics or Chemistry are impossible to reproduce (numbers people get by taking outlier results or even more often by tweaking the data).

When it comes to softer sciences like psychology it's even worse. It's crap.

It's sad, but I think the world desperately needs a *free* alternative to the biggest publishers out there like Nature or ACM or all these things. That free alternative has to be funded by universities and governments globally. This entity should only allow papers that present clear experiments that are reproduced elsewhere or under supervision.

This would greatly enhance the quality and reliability of papers.

Yeah its very true, the incentives are screwed. I think you're touching on the key difference here. Someone like Euler would have had to been forced not to do math, it was his passion. But you have all these "scientists" going through the motions doing "science" because its their job. Passionate individuals will always be rare and the worse part is that the current scientific system in place is tailor made to root these passionate individuals out. A good modern example is Grigori Perelman.

Outside of math, even passionate people need funding.

>You think it's much different for quaternions

It feels like it should be. Maybe the following is just the naivety of a novice looking at experts they don't understand.

Learning numbers, integers, rationals, and real numbers, introduced so much power with each step, to the point that every child is expected to know the basics about real numbers. Maybe not what they are theoretically, but the basic ability to do something like .5 * pi or root(2)^4. They likely never dig any deeper, most don't really get the idea of never ending never repeating decimals, but they are able to work with them on a simple level. For most fields, an introduction only requires this level of math.

When one does move to the complex numbers, it opens up far more possibilities. Fourier transform is everywhere, to the extent many use it without having the math to understand how it does what it does. More complex problems, and I mean outside of the field of math, only have general solutions if you allow for complex numbers to be used. These are difficult, mapping from C to C requires 4D to represent and thus are much harder to visualize, but people still struggle through it.

When I realized that complex numbers weren't the end, but the second step in a tower of infinite height, I wondered what otherwise unsolvable problems needed higher levels from that, just like how many problems needed complex numbers. The difficulty working with them grows, though somewhat given C to C is already 4D, we have already reached the limit of 3D viewing power.

Yet they are rarely used, and higher levels used even less. Maybe there is something fundamental that makes them less useful, far weaker than complex numbers. But from a viewpoint of a novice, I find that surprising.

Like the Eiffel Tower or Burj Khalifa, the algebra tower only has 4 levels (Real, Complex, Quaternion, Octonion) before it shrinks to degeneracy, and level 2 (Complex) has the best balance of dimensionality and power. Adding dimensions adds power, but linking the dimensions adds constraints on allowed structures.

https://en.m.wikipedia.org/wiki/Composition_algebra

> Learning numbers, integers, rationals, and real numbers, introduced so much power with each step, to the point that every child is expected to know the basics about real numbers.

The amount of additional power you get from real numbers is zero, and in fact it isn't possible to work with them because specifying an irrational number takes an infinite amount of time and space.

They give you additional power in the sense that they let you give names to the exact answers to certain equations, but not in the sense that you can manipulate those equations any better than otherwise.

> When I realized that complex numbers weren't the end

But... they are the end. That's the point. We call that the Fundamental Theorem of Algebra: every solution to every equation takes the form of a complex number.

Quaternions do not generalize from complex numbers in the sense of the progression of the numeric tower from integers to rationals to reals. That is known to stop at the complex numbers. They generalize from complex numbers in the sense of functions that scale and rotate two-dimensional images. Quaternions are a way of expressing functions that scale and rotate three-dimensional images. They are familiar to most people who have taken calculus under the name "vector cross product".

(And for completeness, while there are octonions, the full generalization of "functions that scale and rotate arbitrary space" is matrices, which again people tend to be familiar with.)

Not sure what the point is you're trying to make.

All I said is that as soon as you release a paper you fall in a niche of some topic (unless the paper is super generic) where the number of people with the expertise allowing them to review it is super small.

Quaternions or complex analysis where just examples where, even if not strictly experimental and more theoretical, if you're pushing the boundaries of knowledge the number of people able to review what you wrote and concluded isn't that big.

I know that at least in AI/ML there are reproducibility challenges, I even had a course during my masters where we had to reproduce a paper. Not perfect, but some disciplines try to address that. AI/ML has a nice feature of publishing almost only in open conferences/journals, there are not that many closed publishing venues in this field.

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