I just described 4 years of calculus studies in one paragraph, you are welcome.
And why would you care about interpolation? There are a few important lessons it teaches.
1. Avoid looking at the big picture
What would you do if someone told you to build a computer? From nothing, including manufacturing.
There is only one answer to this. It is very unlikely, even for those most knowledgeable, to understand how the entire computer works at once (that’s why we built computers in the first place.)
So what does the computer consist of? Well — processor, motherboard, memory, applications. All very complex things.
What does the processor consist of? Well — some plastic board, transistors, some logic. At least plastic part sounds simple. Silicon is quite cheap these days.
So if we’d had the board and made some simple transistors, what about the logic? You would be amazed how simple it is — in fact so simple people build it in Minecraft.
Now let me stop there. It was just an example, don’t go building computers just yet.
The point is — if you look at the problem as “going from A to B”, with no stops in-between, you are unlikely to get there.
Applies to programming. Any kind of system. Any industry.
When faced with complexity — don’t panic, simplify, and pretend to know what you are doing.
2. Don’t be too eager
Hint to the previous hint. When dividing problem into smaller issues, don’t overdo.
Simplify problem only if it makes sense. The moment you know what to do, stop.
If you go too far and divide a complex problem into hundreds of small issues you will create a new problem for yourself. Exhaustion.
Imagine you are a painter. You have an amazing artwork in mind, beautiful landscape, very breathtaking. You decide to go step-by-step on it. Infinitely small steps, each executed with equal detail and dedication.
You will run out of stamina by the third pebble or rock in the corner of the painting.
They will possibly be the most beautiful pebbles or rocks ever painted. But they are just pebbles. You lost all your energy, and you are not even close to the main part of the painting.
Divide into smaller steps only if it makes sense. Human perception is limited and, at some point, others will not even notice your attention to detail and complex approximations.
(You’d think it is obvious. But I am not taking that risk. Seen too much.)
3. Apply to anything
Yes. Points 1 and 2 apply to pretty much any complex task.
“You said that just to make it relatable to a wider audience.”, you may say.
That is correct.
But I also said it because it is true. Project management. CSS keyframe animation. Responsive design breakpoints. All these, and more, have it in common.
You get much better and faster effects if you break down the complexity into smaller steps. Smaller, straight lines, that in the end take you from start to finish (exactly how to divide different types of problems into smaller steps is a matter for another read.)
If you enjoy learning, feeling smart, or simply like nice pictures, do yourself a favour and read through interpolation and animation in-betweening.
Not only you will see a great application of interpolation, but also find out a bit about making imperfect approximations appear much smoother than they are in reality.
As I like to say, as Stephen Hawking once said, as someone said to him — for every equation (or mention of math, I presume.), audience is reduced by half.
So if you did get to this point, know that I am proud of you. Probably not many did.
That is all for now. Although I do hope to return to this in the future. Especially to the real-life applications of maths in development projects (it is not as common as some would believe it is.)
Thank you for reading. I hope you learned something new (or at the very least enjoyed the pictures!)