Awesome Kalid, Thanks a lot for this great article.
another read, well worth it kalid. i’ve binge read most of your website recently as if it were breaking bad.
that being said, i’ve been bugged by something. the idea that intuitive explanations are helpful when independently learning technical ideas. i’ve always viewed intuition as a sort of mirage to a logical understanding. so i’ve always taken the opposite approach. when learning math, physics, compsci from a textbook i pay attention to my logical insights doing my best to ignore my intuition until i feel like my intuition has gained credibility. your site shows how the creative nature of intuitive explanations are refreshing and helpful when being covertly grounded in logic, but should one apply this intuitive method when learning something new independently?
sorry for being long-winded.
Thanks Leon, if math articles can be in the same breath as Breaking Bad I’m pretty happy =).
Great question on the role of intuition and raw logic. I view it as a spiral, where we develop one, check it with the other, and keep going. Logic needs to be checked by intuition (does this logical conclusion lead to something absurd?) and intuition needs to be checked by logic (does my initial thought make assumptions which are not true?).
For example, there are things like the Birthday Paradox, which states that in a room of just 23 people, there’s a 50% chance of a shared birthday. People’s intuitions jump out and say “23 people! There’s not a 50% chance I’ll have a birthday with someone” but they’ve made a bad assumption, that it’s only their birthday being checked. In reality, we have (23*22)/2 birthday comparisons (every person in the room against everyone else), which is a lot more than the 23 comparisons you’re directly involved in.
So, it’s a matter of recognizing that initial intuition, and training it when it leads to a logically incorrect result (when intuition is wrong, what assumption is being made that needs to be corrected?). Similarly, for logic, there must be some reasonably natural way to think about a scenario other than “We followed all the steps and got from proposition A to conclusion B”.
I have a bit more here: http://betterexplained.com/articles/developing-your-intuition-for-math/
great response. i suppose the culprit responsible for my different perspective is that i’m an ‘aspie.’ the didactic ‘spiral’ you use explains why i get so much out of your website: while I find the intuitive curves to be much harder to understand than the ‘raw logic’ i get the sense that your increasing intuitive ability.
you’re doing great things for people who are not only neurotypical, but also for those with AS.
Your explanation of power is incorrect. You are describing energy instead. P = energy/time. Lifting 1k lb once = lifting 100 lb x10 when referring to energy, but since lifting the 1k takes 1/10th the time and therefore requires 10x the power.
@Parallax: Thanks, I might not have been clear enough in this sentence:
“In the same minute, suppose Frank lifted 100lbs ten times, while Annie lifted 1000lbs once. From the equation, they have the same power (though to be honest, I’m more frightened by Annie.)”
So Frank took 60 seconds to lift 100x10 pounds, and Annie took 60 seconds to lift 1000x1 pounds. The net energy and time were the same, right? (I could clarify that Annie was pushing the entire minute to lift it up, not that she was done a few seconds in.)
Hi Kalid,
As usual it is brilliant explanation. The way they should have taught in my school some very long time ago :). I also wanted to add that Water Power topic is another area where your Oomph X Often explanation fits perfectly.
Water Power = (Energy /Volume) * (Volume/Time) is more intuitive than the usual Water Power = Flow Rate * Head.