Basically the assumption is that the signal x(t) is equal to 0 for all t < 0 and that the integral converges. And what is a bit counter-intuitive: Laplace transformations can be regarded as generalizations of Fourier transformations, since the variable s is not only imaginary but fully complex. But yeah… I would have to brush up on it again, before explaining it as well. It’s… been a while.

I was at the intersection between mechanical and electrical engineering as well as computer science. And worked in/with (electric) mobility, agriculture, medical/rehabilitation tech., solar energy, energy grid, construction and building tech. As well as some very limited stuff with economics. And I intentionally chose my study courses to be able to work in multiple areas and inter-disciplinary. My latest work is more on the business and management side of things and less technical, though.

What are you studying and what direction are you hoping to head in?

Basically two things: 1. Complicated operations in the time domain like convolutions become simple operations in the frequency domain. 2. It is way easier to handle complex numbers and do analysis with them than with explicit frequencies to the point where some things like stability and robustness can be judged by simple geometry (e.g. are the eigenvalues within the unit circle) or the sign of the imaginary part.

EDIT: I forgot the most important simplification of operations: A derivative in the time domain, becomes a simple multiplication by s in the frequency domain. So solving Differential Equations of the system’s dynamics becomes pretty easy without having to go back into the time domain explicitly.

It seems simpler than the Fourier transform, until you realize that the s is a complex number.

Oh, look at that hornet’s nest. I wonder what happens if I poke it

As someone who worked with system modelling, analysis and control for years… I do think the Laplace transform is easier to work with 🙈🏃‍♂️

It’s a bit difficult to advise on such a thing without knowing the people and their situations, so I’ll keep it as general as possible and mention a few common traps. And it won’t be a clear yes or no, because in the end, only you two can make the decision and take responsibility for your own lives.

When people say, that you change a lot during your 20s (or longer for that matter), it’s because of several things, but I’d say the most important are:

First: Your ability to interpret and regulate emotions (the prefrontal cortex is the last part of the brain to fully develop and continues to do so in your 20s). And with that identifying subconscious emotional wounds and patterns driving your decisions, so you can take appropriate action to change your programming where it isn’t helpful. In a relationship context both of your attachment styles are very relevant here.

Second: Identifying and letting go of values and ideas that have been instilled in you by your vicinity (parents, religion, friends, TV, internet, or society in general) and identifying your own intrinsic values and drivers. Or in other words: Learning who you, yourself, really are. I know it feels like you already know, but that feeling can be deceiving. I for one don’t know of a single person who is let’s say 35 and would claim that they truly knew themselves at 20, let alone 17.

So when you say “It has always been my dream to have a family of my own, and that motivated me to propose: why wait if you know what you want?”, I hear some alarm bells going off. I would advise you and your fiancée to be very introspective, where this want came from and whether it truly aligns with yourselves and with your current situation, or whether it came from external influences. This is hard to do at your age, even if there is a chance that you are both already mature enough in that regard. Also be very aware, what marriage actually means. To you, to her, to others (e.g. is it a box to tick off, or is it a gate to real fulfillment?) and legally.

I read in one of the answers that you haven’t had a real fight yet. A primary predictor of relationship success is your way of conflict resolution. Now don’t go looking for artificial conflict to see how you react. But if you for example were to take things in steps, like moving in together before you get married, these conflicts will arise naturally and you would be able to see how that goes. And even if it goes badly at first, if you are both conscious of it and willing, you can both work on the way you react to and communicate during conflict (and in general) to make it succeed. A small word of caution and something to explore (not assuming it’s necessarily the case here): A pattern I see often in couples who “don’t have fights”, is that at least one of the two is avoiding it. Which can be ok, but not if it means always (consciously or unconsciously) abandoning their own boundaries or values.

What complicates all of that, is what people now seem to call “new relationship energy”. Basically the hormonal cocktail of your system that makes you feel so excited and in love with the other person. This leads people to ignore existing and potential friction and romanticize the idea of a future with the partner. While it is possible to “keep a spark alive” for your whole life, if you do it right, this “energy” for a lack of a better word, will wear off at some point. At which time other factors like communication skills, conflict resolution, the emotional depth of the relationship and value/need/want alignment become even more important.

I could go on and on (what’s your plan for education, jobs, place to live, kids, …), but I think these are the most relevant parts to make a decision with both eyes open. The journey can be magical as you get to know yourself and the other person together and witness and be part of the growth together. But it will get bumpy and how you two can navigate those bumps will determine where you’ll end up. No matter the success, it will be a learning experience. If you are willing to learn and act accordingly.

Good luck you two. And don’t forget to enjoy and experience your lives!

In some places in the world, some people seem to get incredibly clumsy when they’re near open windows. In others, they have very guilty consciences to the point of killing themselves.

\s for clarity

Ich kann in der Sache die neueste Folge der Anstalt (Abriss-Anstalt) von vor ein paar Tagen empfehlen. Dort werden Missstände der Finanzierung und Subventionierung des sozialen Wohnungsmarktes aufgezeigt. Sowie eben auch wo der neueste “Bau-Turbo” an der Realität vorbei geht.