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Comment by dekhn | Hacker News Reader

The extra-credit question on one of my finals in grad school was: "What is the time-resolved fluorescence of a fluorophore in 4 spatial dimensions?" We had covered 2D and 3D cases in class. my housemate started the question on Friday night (after finishing the regular questions) and was done some time Monday- she said it was pretty hard problem that involved deriving several new equations for 4 spatial dimensions, throw in some tensor calculus, finally some ugly integrals, and then out pops an analytical expression.

I didn't even attempt it because I knew it would be beyond emotionally trying.

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Do you come from a parallel universe with an extra spatial dimension

Fluorescence is spectrum shifted retransmission.

Energy arrives on some wavelengths, it departs on others.

"Three spatial dimensions" Vs. "Four spatial dimensions" is suggesting the existence of a further spatial dimension orthogonal to our own and is a bit fanciful, however ...

It's legit to look at the evolution of analytic forms from 2 to 3 to 4 to higher (N) dimensions not just for the fun of abstraction but also for the application to phase spaces [1] .. where systems are described using multiple independent orthoganl dimensions to plot the system state at any time and the transitions from one state to another.

I see no issue with looking at energy transposition through phase space, and there are applications.

[1] https://en.wikipedia.org/wiki/Phase_space

Man, I gotta try reading the harder Greg Egan novels again. I'm fine with the biological and even some of the topographical stuff, but when he starts basing character development on actually visualising shifting through orthogonal dimensions like what you're talking about, my brain just exits via my arsehole and I give up.

Greg Egan, Matt Parker, myself, and a slew of others (eg [1]) all attended math and physics classes in what some astronaut called the city of lights and the most isolated city in the world ...

[1] https://www.youtube.com/watch?v=laKp1XeEF74

some of us also appeared in a film with Nicole Kidman

As a WA-native I was aware Egan was from Perth, and though my respect for his desire for privacy always wins out over the cult-of-personality, I'm still kinda chuffed I live in the same remote city as a favourite author.

(And, though I adore the poetry, I believe Perth (to Adelaide, 2131km) is beaten in isolation by Wellington (to Sydney, 2225km).)

I'm stunned and baffled as to what the Nicole Kidman movie could be though; unless you're talking about the character Matthew Parker? I hope you're not also a celebrity Mr/Mrs defrost as I confess I've no idea who you could be :S

seems like they are looking in multiple bands hence the 4 spatial dimensions

"Our approach differs from previous work by combining 3D and spectral super-resolution simultaneously with readily available fluorochromes as well as operating in a wavelength range where biological autofluorescence is minimised."

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3105105/

No, 4D space. Like, you can go forward and back, left and right, up and down, and yimlo and olmiy. We don't have yimlo and olmiy here but I'm sure somebody in 4-space is reading a copy of "Flatland" right now.

The problem wouldn't make sense if you're treating wavelengths as dimensions (and is a far easier problem).

Well, this projection of me does.

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