While I work as a programmer, my degree is in Physics.
I always have a notebook. I carry a small one in my back-left pocket, and take care always to have a pen.
I have a regular-sized notebook that I carry in my computer bag, that has graph paper rather than just lines for text, however as you say I don't have it with me.
With scientific notebooks, what's important is not to be neat, but to write it down so it's not forgotten.
At one time, for inventors, it was crucial to record the date upon which one invented something, however the US patent law was revised a few years ago so that we have "first to file" rather than "first to invent".
I even do stuff like take notes during TV commercials, if I see a product advertised that I might like to buy.