20 days minimum by law in Italy (plus sick leave when needed), in practice though it's more like 28 days for most jobs. Excluding weekends and national holidays of course.
Actually in Italy you don't pay a dime, unless you want to. The level of care you get varies by region, but is generally pretty good, especially for regular, mass events like birth.
My experience is the same, L5-S1 and unfortunately I had surgery (bad decision, but had started developing nerve damage), which just replaced the herniated bulge with a permanent internal scar, having more or less the same effects. ;)
You learn to live with pain, and adapt to it. You learn that some activities are off limits, and will probably always be so. The trick is not to start feeling diminished, not fall into depression by comparing yourself to a mythical healed self, and learn to appreciate the life we have, which even with a bad back is still incomparably better than what the rest of humanity experienced for most of its existence on Earth.
There are ways to get better though, if you don't despair: after 10 years of trying countless practices and remedies, a combination of McKenzie exercises and acupuncture is finally working, allowing me to lead a mostly normal life (eg lots and lots of exercise and just refrain from cycling, contact sports, or bumpy activities like offroading).
My suggestion is to try that with absolute dedication (eg 100 repetitions spread over each day, weekly acupuncture sessions), and if you have no improvements in a couple of months, try something else. Improvement is possible, it just takes a lot of effort and time.
The Land Rover in question is probably a Defender, with a design substantially similar to the original model from the '50s. It really is a refrigerator on wheels.
A really nice project, I might build one for my daughter.
I used to have something similar when I studied Architecture: my drawing table was always covered with thick yellow paper kept in place with painter's tape, on which I jotted down notes and sketches. This is much more practical, as you don't have to cut a new sheet of paper when the old one is too dirty/full.
Or just recognize that three consecutive numbers mean you divide by three and get the median of the three numbers. So 69/3-1, 69/3, 69/3+1, giving 22, 23, 24. No algebra involved, you just need to interpret the problem and build a tiny model in your head. Exactly like (some kinds of) programming.
Amusingly, I taught a college math class many years ago. A question on one exam was:
x^3 = 27
One student solved it in the following way:
1^3 = 1
2^3 = 8
3^3 = 27
ans = 3
There was a meeting for the teachers to discuss grading standards, and I brought up my student's answer. I got a number of responses:
"That's not algebra."
"The student obviously doesn't understand the problem."
And so forth. Being somewhat of a punk, I asked if any of them had, in their years of teaching, actually taught their students to recognize when an answer is "algebra" or how a right answer of 3 differs from a wrong answer of 3. It wasn't a pleasant discussion. This was a university with a prestigious math department, and I was just some guy off the street. I chatted with my students the next day. None of them had ever been told what it means to "show your work," or any of the other important trappings of school math. They either did it or they didn't.
Thinking about it more, I would have sidestepped the issue completely, by changing the problem to:
That's exactly how I solved it. I'd consider myself a pretty decent programmer, but I did poorly in algebra and calculus at middle, high school, and university level.
Give me "x + (x + 1) + (x + 2) = 69" and I wouldn't know where to start. I could probably turn that word problem into that equation, but I would have no idea how to actually solve the equation algebraically.
But given the word problem alone I knew to divide by 3 and add the neighboring numbers. Now, actually dividing by 3 I'd need to use a calculator or spend a lot of time with a pencil and paper, but at least I knew the steps to solve it.
I'm awful at rote math and mental math, which is why I'm thankful I can make the computer do it for me.
Are you saying that if the word problem was "2 consecutive numbers and a third number that was five higher than the second number" you'd be unable to solve it?
"Tricks" work for simple cases. Algebra works for all cases.
Yeah, I would be unable to solve it, given that I'm pretty sure there is no solution if we assume that "consecutive" implies integers (and I'd be curious what 'consecutive' means if we don't).
If instead we made it "2 consecutive numbers and a third number that was five higher than the second number add up to 70" (i.e., 21 + 22 + 27), that's easily solved using 'tricks'. Really, the trick mention (which is what I did in my head, too) is just a rephrasing of the algebra. That is, I would subtract 4 off of the thing that is 5 higher (so that it's now 1 higher; the problem is now the same, get 3 consecutive integers), subtract 4 off of the number I'm trying to get (so 66), so the problem is now 3 consecutive integers that equal 66, and solve the same way (66/3 = 22, so -> 21, 22, 23), and then just add the four back in to the highest (21, 22, 27).
You're right, my mistake. That "five higher" should have been "four higher".
The thing is that your solution is the algebraic solution. You're simplifying an equation by balancing both sides, when you subtract four. Just from our perspective, you simplify to a still difficult state, instead of the easiest possible state.
Algebra is just a way of formally stating what you did, and then offering some simplifications that speed up the process. Or offering more powerful methods that making solving more difficult problems easier.
'The thing is that your solution is the algebraic solution'
I agree. That's why I said
'Really, the trick mention(ed) ... is just a rephrasing of the algebra'
Just because you do number juggling in your head rather than write it formulaically doesn't make it an inferior technique, or make it not algebra, which was my point.
> Give me "x + (x + 1) + (x + 2) = 69" and I wouldn't know where to start.
You memorize a few rules about what things you're allowed to do, then you apply the rules to simplify the problem in front of you. Sometimes, the hard part is that you don't know one of the rules you need to know. Other times, it's figuring out which of the rules you need to know that you should use. By practicing lots of problems, you get a good intuition for which direction to go, but it's not uncommon with more difficult problems to take the wrong way and end up confused.
First, we're allowed to drop the parentheses with addition (the "associative" rule for addition), so
x + x + 1 + x + 2 = 69
Now we put the similar terms together:
x + x + x + 1 + 2 = 69
How many Xs do we have? Three. Another way of writing that is 3x. So replace that part. Also, 1+2=3, so we'll replace that as well. "Apply rule and replace" is pretty much the most fundamental mathematical operation.
3x + 3 = 69
Let's get rid of the 3 by subtracting it from both sides to keep the equation balanced. On the left side the 3 cancels out (that's why we did this). On the right, we get 69-3, which is 66.
3x = 66
At this point, we just divide by 3 and simplify.
x = 66/3
x = 22
Our numbers are x (22), x+1 (23) and x+2 (24) according to how we listed them in the original problem.
Very well put. I have a similar (slightly younger) age, and often pose myself the same set of questions on speed, tooling, typing. Needless to say, my answers are very similar to yours.
As for the Design Process, it works in the exact same way you describe in other fields like Architecture, which I studied and practiced ages ago at a more than decent level.
Money (VCs'), the myth of the young billionaire, and a few other things are probably what make developing different.
Yeah, my first reaction was the same, mentioning them in the top of article while mentioning all other contributors as a note in last paragraph felt like wanting to take all credit.
But then I saw it was published on a ".de" website. You can expect it's targeted at a german audience, who naturally feels interested in knowing which part their country played into this (mentioning others just after wouldn't have hurt, though).
