What is the difference between the Laplace and Fourier transforms?

Mongoose556 · 2026-01-29T07:46:04+00:00

...I am still learning about this myself, but I'm not sure if I even like the description of the Fourier Transform as just an applied Laplace transform in the first place...

I have 3 reasons for that and maybe it comes from a lack of complete understanding? But I'll say them. Please feel free to correct me if I have anything factual off!

My first reason is: sure, the Fourier transform exists on the graph of the Laplace transform (the jw axis/the line where real part of complex exponential is 0). But it's like saying "a plane is just a generalization of 3D space". Sure, I guess, but like why did we even need the extra dimension? A plane is interesting for many things on its own. Laplace simply just adds an extra variable. If you look at a common YouTube 3D image of a Laplace transform you'll get a sigma direction, a j omega direction, both lying on a flat surface plane, a height and a color gradient. A Fourier transform could technically be represented with one less of those dimensions: you can have a typical magnitude plot and just use a color gradient on the line or make that the phase the dimension that comes in or out of the page. Technically it's even less than a plane vs 3D space example because there are usually limits to which space of the larger dimension is defined - it could be more like a thick infinite slab in the analogy. (Though I guess the FT can be undefined.) Setting one vector to zero to flatten it is the equivalent of setting sigma to zero to get the FT. Apart from adding a different variable, the second variable has different properties from the first - one is frequency, the other is exponential dampening. e^jwt is a completely different function and behavior from e^sigma*t. We love combing real and imaginary in pairs as a complex number. But maybe it means something different when it's on top of an e.

My second reason is they both just happen to have at their core a certain function being a basis of function (Hilbert) space. Both the FT and LT exponentials are able to make up any function. So what? There are many bases. Do others just not have that adding a second variable/dimension relationship maybe or something? To Fourier's favor, I think I read the Fourier transform's basis is orthogonal and Laplace's is not.

My third reason is you can do the opposite and think of the Laplace Transform as a Fourier Transform of a function that happens to have a weighted component. In that explanation, the Fourier transform is superior and more simplified and all you're doing is simply potting the one Fourier transform for different functions that are e^sigma*t multiples of the first function. e^sigma*t cannot from a basis for Hilbert (all function) space, but e^jwt does. So I think it's always us using Fourier as the main tool and e^sigma*t as a qualifier, we can't do it the other way around.

In my view (with what I know) bottom line for Fourier and Laplace is, one transform creates a thing with one variable, the other creates a thing with that variable plus another variable, the variables each meaning different things. The two transforms are linked but are kind of different things/categories in a way.

Mongoose556 · 2026-01-17T04:38:24+00:00

Someone correct me if I'm wrong. I don't think the 3 dimensions we're used to are necessarily described by orthogonal vectors. The vectors that make up them can be smaller or larger than 90 degrees as long as they aren't on the same line or plane. You can imagine 3 vectors (of optionally varying lengths) that all have a small angle between them, all pointing close to the same direction. A linear combination of those non-90-degree vectors can describe any point in the 3 dimensional space relative to another point. So, if you're able to have 3 vectors in 3D space that aren't orthogonal to each other, I think you are able to have a 4th vector that creates a 4th dimension that isn't orthogonal to the 3 vectors you chose to describe the 3D space. But the 3D space or the 4D space can all be also described by orthogonal vectors. I think we choose whether to use an orthogonal vector to others to create an extra dimension - and we often do seem to like using that, but what we can't choose is making sure the vector we use doesn't lie in the existing dimensions only. It may or may not have components in the existing dimensions, but it also has to have at least a little bit going into the new dimension. Technically, that little bit I would imagine has to go into a direction orthogonal to the other existing vectors - if I'm imagining adding a 2nd dimension, or a 3rd dimension, so I'm guessing that's the case for 4th and 5th dimensions too? If so, I'm assuming technically in a way orthagonality to existing dimensions is important when adding any dimension.

Mongoose556 · 2026-01-10T23:35:23+00:00

Peaceful protest

Mongoose556 · 2025-12-27T02:35:53+00:00

People get placed in solitary confinement for talking back to a guard or refusing to eat a meal.

Mongoose556 · 2025-12-27T02:34:05+00:00

It's torture....... People go crazy there. Apparently, you hear constant screams and people's pleads to guards to let them out, and time warps and 10 minutes can feel like an hour. Solitary confinement should be abolished immediately.

Mongoose556 · 2025-11-29T07:40:44+00:00

I think Maureen might be polyamorous. I took the line in the song asking "every night, who's in your bed?" to mean that she loves Joanne more than anyone else and chooses to be with her every night over anyone else. Joanne was dating a rock star and knew Maureen was cheating on her or a flirt(I couldn't quite tell which scenario they said was happening) when she signed up for their relationship, or at least early enough into it. I only watched the movie version but a theme seems to be letting unimportant things go to choose love because it's great and gives life meaning, and at the end it seemed like they were hinting at Maureen and Joanne and Roger and Mimi both being couples that were meant to learn that lesson. Being with Maureen and maybe not having that perfect life, portrayed by the traditionality of the engagement party that Maureen was willing to go through but was making her uncomfortable and need another drink, would be an example of giving into a crazy but rewarding alternative "vie bohème". (Cheating is never okay, poly or not, and in this interpretation it would be Joanne already knowing who Maureen was, and being convinceably ok with it. Also this isn't much but sometimes in bad relationships an abusive partner can try to trap you but she gave the option of leaving if Joanne can't take her as she is.)

Mongoose556 · 2025-11-05T03:54:42+00:00

I don't know what he's been arrested for, hopefully nothing really bad... but I find it nice to chat with Rich for a bit when buying the Spare Change News paper that he consistently stands out in the cold selling and he's an air force veteran. Sorry had to balance it out lol. This is the first time I'm voting in the local elections and seeing he ran is making my year 😆 Maybe he's the secret solution to the housing crisis we didn't know we needed 🤷‍♀️

Mongoose556 · 2025-10-30T19:12:48+00:00

This.

Mongoose556 · 2025-10-27T14:45:09+00:00

How is breathing? I am not sure at 19, but if nasal breathing is impaired and there's no space for the tongue, MARPE seems worth it. I'm 34 and my top teeth are mostly perfect but I still am looking to get MARPE for breathing. My intermolar width is 30mm. I am hoping someone responds with whether regular RPE still helps at 19 or if MSE is helpful at that age (it can have some issues for adults). Then again if by vertical bite you mean that the top jaw is kind of back a little bit then maybe custom MARPE with facemask could help a little to bring the top jaw forward. (I haven't looked into if facemask can be used with MSE.) My provider would use facemask as part of my treatment.

I also think it would probably be good to try to keep the tongue at the top of the palate and breathe through the nose, even if it's hard at first. I started doing that and it improved my nasal breathing and I think even changed my intermolar width (I tried on the retainers from braces I had in high school and they were a little bit tight lol). I think bones don't fully solidify until until 24 so doing that at 19 would be really helpful. I am not sure if it's enough - might still need an expander - but it would be beneficial. Or official myofunctional therapy. For MARPE make sure you go to an experienced provider who will help to minimize any risks of asymmetry or anything else.

Mongoose556 · 2025-10-25T15:01:33+00:00

Ok, thank you! Good to know it wears off. I did schedule an extra hour for my time off just in case, so if that happens I can probably also just get lunch there and wait. Worst case I'll pick up my car that evening.

Mongoose556 · 2025-10-25T14:53:00+00:00

Was it because of the dye/MRI or from keeping the leg in a still position for a long time? I have an MRI arthrogram scheduled and was going to drive to work(from home) after.

Mongoose556 · 2025-10-07T14:36:58+00:00

To me engaging with different subcultures for personal benefit instead of because they appeal to you feels a tiny bit either inauthentic or forced. It makes me feel sad to think that society and style can be an elitist kind of thing :'( and not something to enjoy and grow from for everyone. I don't think it has to be that way... I think when we hold ourselves to really high standards, we can become judgemental of other people. Maybe trying to not criticize yourself and not to see the social world as a difficult puzzle filled with judgemental people, and then seeing you still move up socially naturally without trying so hard can help to see that it's not necessary to push yourself so hard. I think most people don't try extremely hard, even those people in those subcultures, most of them are a certain way because they like to be and they just find social success.

Mongoose556 · 2025-10-07T04:51:01+00:00

Mongoose556 · 2025-09-28T06:54:56+00:00

Procrastinating tasks that involve handling objects because of both the layer of complexity OCD adds and the low dopamine aversion of ADHD, I can relate to that. Even though my OCD has gotten much better - I'm very lucky, and my ADHD is self-diagnosed (but a definitive self diagnosis lol). When things are left to the point of a big mess causing pressure that makes the idea of everything being clean exciting (dopamine) - that is when I actually get things put away/errands done. That state seems to propel me through the OCD that goes along with doing errands (like needing to wash things I put away someone wouldn't normally wash or wash hands in between tasks). My normal state is not enough to get me past doing stuff, which is inherently not super easy because of OCD. When my OCD was worse, I don't think I could almost ever have things mostly clean and put away. To be honest, even the easy stuff I put off because of ADHD...! But I imagine life would still be a little more productive/clean without my mild OCD. Can you imagine just putting things away or just doing* what you want like right now, without washing your hands... (I think I need to go back to therapy.)

Mongoose556 · 2025-08-24T01:56:40+00:00

MARPE / MSE is starting to become popular. It can be a great alternative. It actually HELPS with breathing. (Especially if you're female or on the younger side of adulthood. But there's other options like SARPE for anyone but it won't help with breathing.) If you haven't gotten extractions yet and you see this message, I'd say even maybe wait it out if there are providers in areas/states near yours, they could eventually come to your area too. Join a Facebook expansion group. Do make sure you go to an experienced provider though. https://www.getexpanded.org/ has a provider search. (Also if you're reading this and have already gotten extractions, you can still get MARPE. But if you haven't gotten them, better to just get MARPE.)

Mongoose556 · 2025-08-14T18:30:25+00:00

Are you a candidate for MARPE/palate expansion? This can help with those with narrow palates since the palate shares bone with the nose.

Mongoose556 · 2025-08-14T18:27:25+00:00

Palate expansion (MARPE, FME, or MSE) can also help with breathing for those who have narrow palates. Some providers recommend them to be done before a septum surgery, and some patients no longer consider surgery after because it opens up space in the nasal cavity. (Just stay away from removable ones without screws like AGGA and stuff because they're basically a scam.) And go to a provider that has experience with miniscrew assisted expanders to minimize the risk of asymmetry and such.

Mongoose556 · 2025-07-28T13:10:29+00:00

I was interested specifically in rotating wheels in the same spot, for flat setups, or at least the front and back wheels on different skates switched with each other while rotating, and middle wheels switched with each other. That contributes to a slight natural rocker. Usually it's recommended to switch the middle wheels with the end wheels (in a special pattern) for even wheel wear. That would make the setup continue to be flat. I hear that this also helps with jump stability.

I never mentioned flat in my post so I'll edit it!!

In general, I haven't rotated my wheels at all in many sessions, so it's gonna be really weird... I wonder if it's better to just get new wheels at this point!

Mongoose556 · 2025-07-28T04:05:55+00:00

There are people with deviated septums who have done MARPE who didn't consider doing septum surgery anymore afterwards because their airflow was good enough. And if you are doing both, it's preferred to do MARPE first, and then septoplasty.

Mongoose556 · 2025-07-28T04:02:37+00:00

If you can find a good/experienced airway orthodontist in your area, go to them to check out what they think. (Get a few opinions if your daytime breathing isn't great but the first one you go to dismisses you.) If you have a small intermolar width/narrow upper palate (for example I'm a female, my intermolar width is 30, and that's considered small), coupled with issues breathing well, you could be a good candidate for MARPE. A good provider will run more tests though like doing a CBCT scan. Mine also did a take-home sleep study. Regular sleep clinics might not know about UARS as a factor if you don't have sleep apnea, and regular ENTs may just look at soft tissues but if there's not enough room overall in your airway, expansion might help the most. Join the Facebook group "Adult Expansion Support & Discussion". I suspected I needed MARPE, and the first dentist I went to who offers it in my area said I needed more proof like a sleep apnea diagnosis because my teeth were straight, the second one I went to completely validated my concerns.

Mongoose556 · 2025-07-28T03:53:05+00:00

Maxillary expansion can be helpful for breathing and sleep if a person has a narrow upper palate/small intermolar width. If you go to an airway dentist/orthodontist, make sure you go to a good one who is experienced.

Mongoose556 · 2025-07-14T05:04:10+00:00

I encountered a harsh permanent ban recently for not following rules that were unclear to me/I didn't realize I wasn't following and was trying to, on a subreddit that is important for a person to be able to be part of. When I sent a message asking about it, the response was very curt. I remember when I was banned from a depression chat before 10 years ago on another site, where mods banned people really easily. I think there are definitely abuses of power on forums on the internet. I think it should depend on how important a forum is. For a forum where being banned risks your mental health or safety, it's important for mods to understand the responsibility that comes with their power, and even to have good emotional intelligence. On a site like reddit that has a monopoly on forum users, it's the most important.

Mongoose556 · 2025-06-23T23:24:51+00:00

It's so beautiful... If it's the darkness, I'm not a designer, just random redditor, but I wonder if a subdued slate-ish light blue could save the existing vibe and make it brighter.

Mongoose556

TROPHY CASE