I think log to the base 10 of 2 is 0.3010. But that is a 35 year old memory
The natural log of 2 is 0.693. Could be wrong but it's a more recent memory
You did it. Double checked on my calculator.
During my engineering career, never had to pull those numbers from memory.
Speaking of engineering, there is an idiom about someone going non-linear. Non engineers use it all the time. I wonder how many can explain what the meaning of this idiom really is? I admit that I don't know the official meaning, but knowing engineering, I can guess. Anyone want to venture a guess what they think it means?
I teach physics for a living
The log to the base 10 I just weirdly remember from school. The ln2 crops up every year because decay constant times half is ln2. But the data sheet use to say 0.693
I talk about non linear all the time. If I'm correct it's a huge part of what I do. Most students assume all change is linear. Some changes are. If the wire is twice as long it has twice the resistance. But if the wire has twice the diameter it has one quarter the resistance. That's the non linear bit
The twice-as-long wire has to push electrons twice as far through the same size pipe. The twice-as-thick wire is a pipe with
four times the cross section (to carry four times as much flow) and only has to push electrons through the original length. I'm not sure how graphs of the two processes would look.
OK, here's my guess as to where this idiom came from. First, an idiom must have something that its based on to even have gotten started in the first place.
Before there were transistors, there were vacuum tubes. Now a vacuum tube is a voltage amplifier. Put in a small sine wave signal, and get back out a larger sine wave signal. But there are limits to what can be injected into the tube. The operating range of inputs is expected to be in the linear portion of the vacuum tube. If you should drive this vacuum tube too hard, the vacuum tube goes into what is called the non-linear region. And if this was an amplifier being used for music, for example, while staying in the linear portion, the music gets louder and louder, but it does not distort. Once it is turned up too high, the amplifier enters non-linear mode, and the signal starts to distort badly. Maybe you have experience hearing a teenager play their music so loud that it ceases sounding like music and becomes ugly noise. This effect can be heard with transistor amplifiers too, but its been around so long, that I think that it started with vacuum tubes.
My guess is that early engineers (we are all over the place) started calling this region by the phrase "going non-linear" and others liked the term and started to apply it to all sorts of things/people going wrong.
Now this is my best guess. I can't find the source in the online free idiom dictionary. But who else but an engineer would even think up this term?
In thinking of vacuum tubes, my thoughts have moved to wondering just how big the Sony A9 camera would be if it was based on vacuum tubes and the memory cards based on ferrite core memory. As a clue to how big this would be, the first large computer, named ENIAC, built in 1945, and which was used to help win the war, is described here:
https://en.wikipedia.org/wiki/ENIAC
hint: The Sony A9 camera has way, way, more computing power than ENIAC and it has way, way more memory.