Based God Updated 2025-07-16
Someone who is not a pussy.
Someone once called Ciro Santilli that: archive.is/W1ocv. It's an overstatement, considering that Ciro's parents have some money. Not infinite. But still. Changes everything. A real Based God is someone like Charles Bukowski, who had to work decades at the post office.
Ciro Santilli believes that there is a close link between the ability to create disruptive technology, and the desire to find bugs/exploits in systems.
Both of them destabilize society and enterprises.
Some examples:
And yes, this sometimes leads into a fine line between legality and illegality:
Ciro feels that this resonates a lot with his OurBigBook.com.
Supercut:
The minute I dropped out I could stop taking the required classes that didn't interest me, and begin dropping in on the ones that looked far more interesting.
And much of what I stumbled into by following my curiosity and intuition turned out to be priceless later on.
Because I had dropped out and didn't have to take the normal classes, I decided to take a calligraphy class to learn how to do this.
None of this had even a hope of any practical application in my life.
If I had never dropped in on that single course in college, the Mac would have never had multiple typefaces or proportionally spaced fonts.
Of course it was impossible to connect the dots looking forward when I was in college. But it was very, very clear looking backward 10 years later.
Again, you can't connect the dots looking forward; you can only connect them looking backward. So you have to trust that the dots will somehow connect in your future. You have to trust in something — your gut, destiny, life, karma, whatever. This approach has never let me down, and it has made all the difference in my life.
Then:
You've got to find what you love.
And that is as true for your work as it is for your lovers.
Your work is going to fill a large part of your life, and the only way to be truly satisfied is to do what you believe is great work.
And the only way to do great work is to love what you do. If you haven't found it yet, keep looking.
Don't settle. As with all matters of the heart, you'll know when you find it.
And, like any great relationship, it just gets better and better as the years roll on.
So keep looking until you find it.
Don't settle.
And:
When I was 17, I read a quote that went something like: "If you live each day as if it was your last, someday you'll most certainly be right."
It made an impression on me, and since then, for the past 33 years, I have looked in the mirror every morning and asked myself: "If today were the last day of my life, would I want to do what I am about to do today?"
And whenever the answer has been "No" for too many days in a row, I know I need to change something.
Mirror and morning are not required though, a computer screen will do just fine: www.reddit.com/r/depression/comments/6jtamj/im_at_work_just_staring_at_my_computer_screen/
And then he quotes form the Whole Earth Catalog, a paper Atlas from the '70s he admired:
Stay Hungry. Stay Foolish
Dirac delta function Updated 2025-07-16
The "0-width" pulse distribution that integrates to a step.
There's not way to describe it as a classical function, making it the most important example of a distribution.
Applications:
Lie group Updated 2025-07-16
The key and central motivation for studying Lie groups and their Lie algebras appears to be to characterize symmetry in Lagrangian mechanics through Noether's theorem, just start from there.
Notably local symmetries appear to map to forces, and local means "around the identity", notably: local symmetries of the Lagrangian imply conserved currents.
The fact that there are elements arbitrarily close to the identity, which is only possible due to the group being continuous, is the key factor that simplifies the treatment of Lie groups, and follows the philosophy of continuous problems are simpler than discrete ones.
Bibliography:
Video 1.
What is Lie theory? by Mathemaniac 2023
. Source.
Euler number Updated 2025-07-16
Linear differential equation Updated 2025-07-16
The name is a bit obscure if you don't think in very generalized terms right out of the gate. It refers to a linear polynomial of multiple variables, which by definition must have the super simple form of:
and then we just put the unknown and each derivative into that simple polynomial:
except that now the are not just constants, but they can also depend on the argument (but not on or its derivatives).
Explicit solutions exist for the very specific cases of:
Order of a differential equation Updated 2025-07-16
Order of the highest derivative that appears.
Phase space Updated 2025-07-16
This idea comes up particularly in the phase space coordinate of Hamiltonian mechanics.
Control theory Updated 2025-07-16
This basically adds one more ingredient to partial differential equations: a function that we can select.
And then the question becomes: if this function has such and such limitation, can we make the solution of the differential equation have such and such property?
It's quite fun from a mathematics point of view!
Control theory also takes into consideration possible discretization of the domain, which allows using numerical methods to solve partial differential equations, as well as digital, rather than analogue control methods.
Chain rule Updated 2025-07-16
Here's an example of the chain rule. Suppose we want to calculate:
So we have:
and so:
Therefore the final result is:
Maxima and minima Updated 2025-07-16
Given a function :
we want to find the points of the domain of where the value of is smaller (for minima, or larger for maxima) than all other points in some neighbourhood of .
In the case of Functionals, this problem is treated under the theory of the calculus of variations.

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