Gave me shivers reading it. Beautiful example of the incredible mystery of the human mind.

Poof! And the solution materialized. Of course, all the groundwork had been laid. All the neurons primed. Just incredible.

And that formula. Damn.

Isn’t that how most of us are solving complex problems? Building context and then walking away from the desk for a walk, or perhaps while we’re in the shower in the morning or at night, not focused on the problem but our brain working on it in the background until it is brought forward to our consciousness?

There are many similar stories. Famously Tesla's recollection of himself "inventing the inductive motor" while walking in some garden in Hungary, and the discovery of the Benzene ring.

I often do this when I need a good solution to a problem:

Work hard on it for a while, then leave it for one-two days. More often then not this give a way better end result.

That was my thought. Why is it so damn complex? You’d think the solution would be simpler.

Sometimes complicated things are complicated.

the full equation for general relativity would take many pages to print, but Einstein notation makes it much shorter looking. This was not the case here.

Probably looks a lot simpler in A-normal form, with intermediates factored out.

> You’d think the solution would be simpler.

Why would I think that?

It is. Some parts are repeated, the one which caught my eye was (zₐ’(rₐ)²+1)

I mean, if it was simpler it wouldn't have taken 2000 years.

I don't see the correlation here. Is every equation henceforth discovered guaranteed to be more complex than any before it? I hope not.

That formula is just a Mathematica dump. If you read the paper, which is unfortunately paywalled, you'll see the result is the solution to a complex system of equations, which are far easier to digest than the result you see there.

This seems to be a version of it: https://arxiv.org/abs/1811.03792

> Poof! And the solution

...snapped into focus

mind-blown by that formula

amazing what people think of

It wasn't thought of, it was calculated using a computer algebra system. Such systems are very powerful, but tend to be fairly bad at writing things nicely and simplifying, so they often produce insanely big and complicated formulas.

This raises the perennial question of whether product placement is a legitimate source of funding for fundamental scientific research.

After placing an ice-cube in my delicious glass of refreshing coca-cola brand carbonated beverage, I yelled Eureka! and jumped out of the bath.

Is that really how it happened? Is it not inconsistent with the pursuit of truth?

It's really natural, on first mention, to refer to something using a member of the degenerate set of its most unique identifier, right? From that point on, to avoid repetition, mix in antecedents or generic names.

Brands exploit this mechanic in language so that any time a, thereto unknown, good has to be addressed, that identification become advertising. It shifts from being a unique identification of an object/item/thing to a conjuring of the ethos/identity that contextualizes that good as being different from all the others (un)like it.

I'm sure the dude was just having some hazelnut spread and that's how they recalls it but us, like them, are getting hacked. Now if you'll excuse me, the rey--, I mean tinfoil, is starting to get itchy, I need to switch it out.

Hazelnut spread is one of those things that is much more commonly referred to as the brand name. No one says "Reynolds wrap" they say "aluminum foil".

No one says "hazelnut spread", they say Nutella.

No one says "resealable sandwich bags", they say ziploc bags.

Most people would just say "sandwich" unless the spread is somehow critical to the tale. I know it's a quote, but it sounds most odd to me as most people I know don't really brand drop in conversation. Coke is probably the big exception there...

TIL what ziploc bags are. Just called "sandwich bags" here. Cling film isn't "sarran wrap" here either. :)

There used to be a distinction in the US: Saran Wrap was made of Saran and was much less oxygen-permeable than other cling films as a result. In a development that represents some kind of evidence about trademark law, Saran Wrap in the US is no longer made of Saran, due to concerns about plasticizers leaching into food; but it is still sold as "Saran Wrap". Here in Argentina, I can still get cling film made of PVDC, just not Saran-brand PVDC.

> Coke is probably the big exception there...

Even then, it may not be. There are plenty of places where Coke has become the generic name for pop, and doesn't necessarily refer to the brand.

> No one says "resealable sandwich bags", they say ziploc bags.

Everyone says resealable bags. I've never even heard the word ziploc. In New Zealand.

In the US, they’re always referred to as ziploc bags. If you called them something else you’d get some confused expressions.

Do they also not use hyperbole in New Zealand?

Perhaps no one in New Zealand, but New Zealand has the population of a small US state.

Nutella though is a sugar-and-palm/vegetable-oil spread, which - probably accidentally - contains traces of hazelnuts, powdered milk and cocoa.

I don't understand the downvoting of the parent here, which is factually correct and worth noting. It's incredibly unhealthy and this is just down to marketing that anybody eats it. You can make really nice chocolate spreads with your own hazelnuts

The needlessly bad-faith "probably accidentally" is factually inaccurate.

Just to clarify: it wasn't bad-faith, I was just (trying to be) sarcastic, as most of the store-bought food nowadays "may contain traces of nuts and/or eggs and/or celery" etc.

Aha, do note that sarcasm mostly goes down badly on hn, because literal people, and jokes historically frowned upon.

Nothing in that comment is factually correct or worth noting. Do you realize what butter, Marmelade, Margarine or vegetable spreads are mostly made of?

>It's incredibly unhealthy and this is just down to marketing that anybody eats it.

Because a spoonful of palm oil and sugar with hazelnut flavoring is tasty?

I think 13% hazelnuts, 8.7% powdered milk and 7.4% cocoa[0], are quite a lot more than "traces". Sure it could be better, but then you could say that about 90% of products in the average supermarket.

[0]Just went into the kitchen to check

> No one says "hazelnut spread", they say Nutella.

For one thing, Nutella is chocolate flavored. No one would ever even consider calling it "hazelnut spread".

It's both!

https://www.amazon.com/Ferrero-Nutella-Hazelnut-Spread-26-5/...

Yes, I'm aware that it's made with hazelnuts. But in order for someone to refer to it as a "hazelnut spread", hazelnuts would have to be the dominant flavor. They're barely there at all.

(Compare the consistency of nutella to the consistency of peanut butter.)

Since we are splitting hairs, the container list the product as; "Hazelnut Spread with Cocoa". Quite prominently, in fact.

Why would your definition be more valid than the manufacturers?

We are discussing in the context of what people use in everyday language. In the U.S., the use of "hazelnut spread" over Nutella is exceedingly rare. Even when dealing with an off-brand, non-nutella "hazelnut spread".

It's just a writing device, in this case. The contrast of mundane detail and the high calling. Used all the time, e.g. NYT's style has pretty much devolved to the formula “begin with the details, then introduce the central topic.”

>> It's really natural, when first mentioning it, to call something using by a member of the degenerate set of its most unique identifier, right?

Huh? ‘degenerate set’ being what, the brand placement? I likes me some Semiotics, though not sure what this passage refers to.

In the context of a photography site, brand mentions must be a hazard. The author has no problem name dropping an Ancient Greek, Newton, Leibniz, Huygens. Why not Nutella? Rather than increasing the cognitive gap between the auditor (us) and the subject (2000 year old problem), Nutella seems to take the shining brilliance of those luminaries down a notch and in line with the form of writing—a neutral density filter? Haha. Or maybe it’s just a laugh and some color.

I don't know any Semiotics! But, in an effort to drive the conversation, I can be more precise with what I'm trying to say.

I'm working with this informal idea that there is always a relationship between the audience and the speaker. That relationship define a shared knowledge space.

If I am speaking to a group of my friends and need to refer to my brother the set of identifiers that uniquely conveys his identify to my friends might be {brother, Joe, Joe Blow, brother-man, etc}. Any of those identifiers coming from to me specify exactly one person, my brother. The degeneracy is that they equally identify him to the audience.

If you were not that close to me, and I say "brother", you might wonder if I have more than one brother. If you did not know me at all I might say Dr. Joe Blow to identify him and why he might be relavent in some area of expertise. As the relationship between speaker and and audience grows more distant the set size decreases. Inversely, the context-free uniqueness of the identification provided by the remaining identifiers has to be greater, with proper names maintaining greater uniqueness (sorry to the John Smiths of the world!) than nicknames and so forth.

To return to my point, the scientist in question called it Nutella because he does not have a deep relationship with his audience and that is the most unique way of identifying it. I don't believe he was doing anything atypical or nefarious. If he knew the audience well, he could have just said "breakfast", and they would know exactly what he meant because he has the same thing for breakfast most mornings.

The problem is that brands, unlike most proper names(obviously famous people are an exception), have a greater ethos associated with them. If my brother was named Joe Blow or Jim Deal, my unique referencing of him doesn't do much to color the statement around it. This is contrast to how much extra you get when you call a car a Ferrari vs a grand tourer. My point is that advertisers recognize this linguistic norm and exploit it, this is what brand identity is. As such, just the natural mention of a good becomes advertising.

There is a lot to unpack in your response, but I guess it’s your use of the term ‘degenerate’ which confuses me. It’s not common in the Semiotic cannon, and so you say it’s not something you’ve studied.

From your original comment: “...contextualizes that good as being different from all the others (un)like it.”

This is textbook Semiotics. Meaning is not derived from the designation (‘apple’ is the red fruit with the thin skin and firm ...eh flesh. Rather, Apple is not a banana; not a kiwi; not a tomato; not beef; ad infinitum.

It's totally common when talking about quantum states that have identical energies! Which is not helpful at all in this conversation. It's just one of the words in my everyday tool bag and I used it without thinking too deeply.

All that said I just order an intro book on Semiotics. Interest definitely peeked.

Under the US system, at that point the term is now generic, no longer trademark-able, and anybody can use it.

In other words, Brands by definition must be distinct from regular language.

> This raises the perennial question ...

Not really, no. There's no scientific funding riding on your reading this article in a photography magazine.

Specificity is almost always recommended in any creative writing from song lyrics to infotainment like this. It enhances humor and mental imagery, which enhance general enjoyment. That's all that's happening here. Hanlon's razor is your friend.

Do we know the brand of the chocolate that melted when the microwave was discovered? Maybe it's not that important.

Indeed. That is why I like the Nikon product placement a lot better because it just highlights what kind of a problem they create with the decision to have only one card slot.

My eurekas are generally in front of the mirror while using my gillet razor. I do not think the brand of the razor has any influence.

What truth?

I wonder that programming language he used. Many ideas are lost because we don't have something to write it on. That's the good thing about the so-called 'scripting languages' that IMO reduce the latency between idea and its materialization.

It was Mathematica, they provide the code in the paper.

If you're really curious, maybe ask?

Shouldn't be too hard to figure out appropriate contact details. :)

Reminds me of that story about Archimedes.

For anyone unfamiliar: supposedly, while bathing; he suddenly realized the principals of buoyancy. He then jumped out of the bath and ran down the street -- without clothes -- yelling "Eureka!" (I have found it). Not sure if this is true or just a legend, but I doubt we'll ever find out what happened to that Nutella bread either...

Probably should include what problem Archimedes has been stuck on until his realization of the principles of buoyancy gave him a solution.

The King had order a gold crown, and after receiving it suspected that the goldsmith may have replaced some of the gold with cheaper silver. The King asked Archimedes to figure out if the crown was pure gold.

Archimedes could do that by figuring out its density, but to do that he needed to get the weight of the crown and the volume of the crown. Weight was easy, but he had no idea how to get the volume, other than melting it down and reshaping it into a shape whose volume he could calculate. Naturally, the King wanted Archimedes to answer the question without destroying the crown.

His realization that the volume of water displaced by an object that is more dense than water is equal to the volume of the object gave him a way to get the volume of the crown without harming it.

and the crown? or is the crown akin to the Nutella bread.

Brain was doing the computing so that he can eat more Nutella bread. Bummer, he just left the Nutella bread and went programming the solution.

Maybe it should have convinced him to procrastinate instead. Now, I know where all my inefficiency is coming from.

> Mothers! It is there!

Since no one has clearly pointed it out, "¡Madres!" is a multipurpose Mexican expression that rarely has to do with actual motherhood. "Holy crap!" is a good analogy in this case.

https://www.urbandictionary.com/define.php?term=madre https://www.spanishdict.com/translate/madre

Brouwer had similar inspiration from a cup of coffee. In his case, the intuition was that if you stir coffee, there's a "part" of it that stays fixed.

In math terms, f:X->X where X is compact and convex, and f is continuous, has a fixed point (exists x_0 in X, f(x_0)=x_0)

The article says Nutella bread, but I wonder if it was toast. Which I prefer. And the time waiting for the toast allowed long enough for his mind to wonder to the solution.

¡Madres!