KF Math Thread - Discuss Math

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Vecr said:
Ah yes, of course.

If you follow the correct math of the post

You must set the dark variables A and x to the correct values. Using non-Gnostic AI Alien Kabbalah that I'm sure you all have worked out already x = 0.75, and simple astrological numerology brings us to our desired result if A is set to 1.55 recurring.

A x ( 1* 1 ) 6 + 5 = 12
◼
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But if we look at the original question "what is A?" And the answer "12" that means 12 x (1*1) 6 + 5 = ?
 
Sparkletor 2.0 said:
But if we look at the original question "what is A?" And the answer "12" that means 12 x (1*1) 6 + 5 = ?
Click to expand...
First:
SamanthaPrater said:
1 X1 EQUALS 1
Click to expand...
Big X is the speed of light, as you can see. X = c
Little x is smaller than big X, and equals 0.75
Therefore 1X1 = 1 and 1x1 = 0.75 * c

What is this symbol "?"? Clearly, it represents the question of our existence. By the famous proof "I think about stupid math therefore I am" this must equal the value of certainty. By standard axioms this is 1.

The equation doesn't appear to work out, but it can be solved. Note that the number of genes that make a cat orange is 13 + 12 and I saw 2 orange cats yesterday. There are 8 nearby planets that directly orbit the sun and nothing else, and that sun is 1. Hence the formula:
A = 12
x = 0.75

A x (1* 1) 6 + 5
――――――― = 1
(13 + 12) 2 + 8 + 1
◼
 
Hey farmers,

I haven't had the opportunity to read up on any of the starter guides over the holidays, but I have thought about a field I'd be more interested in: 3D Physics and 3D Perspective/Rendering/Lighting maths type stuff. Is there any good skill-tree to get there?

Thanks in advance.
 
Private Tag Reporter said:
Hey farmers,

I haven't had the opportunity to read up on any of the starter guides over the holidays, but I have thought about a field I'd be more interested in: 3D Physics and 3D Perspective/Rendering/Lighting maths type stuff. Is there any good skill-tree to get there?

Thanks in advance.
Click to expand...
There's two paths you can go down: theoretical physics where you try to figure out how the world works, and computational physics/computer graphics where you make computer simulations of the real world.

In either case knowing and being skillful in linear algebra will be of great help. Computers can multiply matrices fast and most of your physics object data can be written as them. Optimising algorithms often involves using matrix properties to lessen the amount of computation necessary. On the other hand, fields like quantum physics are entirely built on linear algebra; and math in general wants to linearize things to make them easier to work with.

Peter Shirley has great books on computer graphics. There's also a great series of lectures at UC Cali on computer graphics on youtube. I don't have any resources for physics simulations, but you'll need a working knowledge of DEs, real analysis and numerical integration/discretization since simulations are basically discrete numeric approximations of integrals and DEs.

Theoretical physics enjoys foreknowledge of functional analysis (for which linear algebra is a prerequisite), but also general DE knowledge too. You can start by deriving classical Newtonian mechanics and restating them using something like the principle of least action. Writing computer sims here was a lot of fun for me and helped me grasp and intuit a lot of physics. Any college level classical mechanics textbook should do.

Basically: linear algebra -> functional analysis, differential equations -> numerical analysis. Chasing maths takes time and is frustrating, but even if you struggle with the maths, it'll help you immensely to better understand the actual application.
 
Private Tag Reporter said:
Hey farmers,

I haven't had the opportunity to read up on any of the starter guides over the holidays, but I have thought about a field I'd be more interested in: 3D Physics and 3D Perspective/Rendering/Lighting maths type stuff. Is there any good skill-tree to get there?

Thanks in advance.
Click to expand...
Screenshot 2025-01-02 123605.png
 
I made some a software list in this thread, now I don't use all these programs/apps I'm posting in this math thread here. But since everything is moving towards AI tools, web apps and cloud computing. I think that these are the STEM software related to math that are "as good as it gets" for running stuff locally. I'm aware that some of them are gimmick-ware, perhaps not the most useful software, but I think it's nice novelty to have if you want to play around with something or have a "doomsday calculator" software suite. Take this list for what it is for: A software dump.
Math Software

The elephant in the room MATLAB, but that is not cheap (well, there are "free" versions out there). So here are my alternatives:
  • Octave (not that bad actually)
  • Scilab (got more packages than octave)
  • Maxima (an old symbolic solver, think of it as an outdated Mathematica)
  • Python with SciPy and NumPy can get you a long way (seems like most machine learning projects are using python, so it might be the "smartest" option to learn if you want a "nice resume", but you can also just lie)
Some simpler stuff:
  • GeoGebra (simple graphical calculator software, also has an APK for android)
  • LabPlot (to make fancier graphs for reports if you care about that)

Electrical circuit simulators (mostly gimmick stuff to check exercises if you are studying, not really for serious work):
Some niche physics stuff (good for undergraduates and high schoolers):
  • VESTA (Crystal structure viewer, if you are studying lattices it might help you see the structures better)
  • PhET (It's made for kids, but it's a good little "learning" app if you are learning physics for the first time, don't underestimate relearning the basics when you are older... you might see things in a new perspective)

Got some obscure software that won't run on modern computers? Just try VirtualBox with the required OS to run it and see what happens.
 
Last edited:
9th year in hell said:
I made some a software list in this thread, now I don't use all these programs/apps I'm posting in this math thread here. But since everything is moving towards AI tools, web apps and cloud computing. I think that these are the STEM software related to math that are "as good as it gets" for running stuff locally. I'm aware that some of them are gimmick-ware, perhaps not the most useful software, but I think it's nice novelty to have if you want to play around with something or have a "doomsday calculator" software suite. Take this list for what it is for: A software dump.
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I'd add to your list SymPy, it's a pretty good free CAS based on Python. I've used it to conduct extremely tedious algebraic manipulations, computing Riemman integrals and antiderivatives, or performing exact numerical calculations and then converting them to floating point at the end to avoid compounding numerical errors.
 
This past month I have been thinking about the Monty Hall Paradox. I first came across it years ago but it came to mind again because I saw this cartoon.

1738155327352.png

It has always been weird to me. I even went so far as to write a short Python program to simulate it over thousands of iterations and my computer was clearly in on the conspiracy against me to pretend this made sense as it agreed with the maths. I will have to try again with dice and pen and paper to confirm this directly with Reality. But ten-thousand iterations for statistical validity may take me some time...

Anyone else find this throws them for a loop? If so, why? If not, also why? The maths is trivial. I have no problem following it. But the implications are bizarre. It's a kind of mental illusion where you appear to have the same event described differently by two contradictory mathematical models, implying that maths is aware of past events. But the awareness is on the part of the person not the maths, that's the illusion.

I still find it crazy. It feels like God's joke.
 
Overly Serious said:
This past month I have been thinking about the Monty Hall Paradox. I first came across it years ago but it came to mind again because I saw this cartoon.

View attachment 6917492

It has always been weird to me. I even went so far as to write a short Python program to simulate it over thousands of iterations and my computer was clearly in on the conspiracy against me to pretend this made sense as it agreed with the maths. I will have to try again with dice and pen and paper to confirm this directly with Reality. But ten-thousand iterations for statistical validity may take me some time...

Anyone else find this throws them for a loop? If so, why? If not, also why? The maths is trivial. I have no problem following it. But the implications are bizarre. It's a kind of mental illusion where you appear to have the same event described differently by two contradictory mathematical models, implying that maths is aware of past events. But the awareness is on the part of the person not the maths, that's the illusion.

I still find it crazy. It feels like God's joke.
Click to expand...
Maybe I misunderstood but I remember thinking about that & the related Bertrand's Box paradox and realizing that both the "wrong" and "correct" answer depend on the starting assumptions.

If you define the problem such that: the gameshow host will ALWAYS choose to open the same door (say, door 3), meaning that door 3 will ALWAYS contain the goat instead of the car, then the chance of winning will stay 1/2 regardless of switching. People then get confused because it isn't clearly stated whether or not that's the case.
 
Lowlife Adventures said:
Maybe I misunderstood but I remember thinking about that & the related Bertrand's Box paradox and realizing that both the "wrong" and "correct" answer depend on the starting assumptions.

If you define the problem such that: the gameshow host will ALWAYS choose to open the same door (say, door 3), meaning that door 3 will ALWAYS contain the goat instead of the car, then the chance of winning will stay 1/2 regardless of switching. People then get confused because it isn't clearly stated whether or not that's the case.
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That's interesting. I recall the first time I wrote my Python program it didn't support the changing probability interpretation. I rewrote it later and found that it did. I had thought I made some implementation error with it (I deleted it) but it could well have been that. I'll look into this difference later.

I find it a fun problem because it's not a question of the mathematics being complexity but of what the maths actually implies.

Separately, this thread should be titled "maths" not "math". It's inherently a plural. You don't get up in the morning and put on your pant, do you?
 
Overly Serious said:
This past month I have been thinking about the Monty Hall Paradox.
(...)
Anyone else find this throws them for a loop? If so, why? If not, also why?
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The way I see it, when Monty opens the door he's bringing new information into the system, and the question is "Should you act on the new information?" Sounds like a pretty clear yes, right? And the only way to "entangle" your choice with the new information is to pick the door that he didn't pick (given that he will never pick your door).
 
Overly Serious said:
Anyone else find this throws them for a loop? If so, why? If not, also why? The maths is trivial. I have no problem following it. But the implications are bizarre. It's a kind of mental illusion where you appear to have the same event described differently by two contradictory mathematical models, implying that maths is aware of past events. But the awareness is on the part of the person not the maths, that's the illusion.

I still find it crazy. It feels like God's joke.
Click to expand...
When modeling natural phenomena, it helps to remember that everything is relative to your frame of reference. By extension, we should look at this probability problem as a series of conditional events.

What makes the odds 2/3 when you switch instead of 1/2 relies on two key details:
  1. Your first answer gets temporarily "locked in". It is a choice out of 3 possibilities. 1/3.
  2. After giving your first answer, the host of the gameshow in the traditional problem opens a door. When he does, he is doing so with the knowledge he is picking a door that doesn't have the desired prize behind it.
The host has to pick based off your original answer (i.e. he won't open the door you just picked), and he will not pick at random (hence eliminating the chance of him revealing the prize door). Since the host has knowledge of the answer, his behavior inherently lacks variability; your decision-making process is effectively randomized while his isn't. By definition, his behavior wouldn't factor into your random probability model since he will behave entirely predictably.
 
Monty Hall is one of those problems that I think is complicated more by how it's phrased than the maths of it.

At the outset you have a 2/3rds chance of picking a goat. If the challenge was "don't pick a goat", you should always switch because there's a 2/3rds chance you picked a goat the first time. Monty opening the door doesn't change your odds of having picked the goat. What it does change is the odds of switching and finding another goat. Since the other goat was eliminated, we know that there's a 2/3rds chance we picked the goat, and a 1/3rd chance we initially picked a car, yielding the following permutations:

Goat -> Car
Goat -> Car
Car -> Goat

This expands to any number N doors, N-1 doors revealed. Say 5 doors:

Goat -> Car
Goat -> Car
Goat -> Car
Goat -> Car
Car -> Goat

I think the probability of "finding the car" is what throws people for a loop, seeming to magically go from 1/3rd to 2/3rds - but finding the car was never the problem. The problem always was "don't find the goat".
 
Briarthorn Addict said:
There's two paths you can go down: theoretical physics where you try to figure out how the world works
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When I was still planning on a physics PhD, I spoke to one of the professors in my department about wanting to do theoretical. This fella looked me straight in the eye and said "In America, all people care about is experimental, you'll never get funding".
 
Thanks for all the responses about Monty Hall. Handing out a whole lot of thunk-provoking reacts right now. The below is an absolutely great distillation of the problem, in particular. It's exactly the sort of thing I'm talking about - simple maths, bizarre implications:

Private Tag Reporter said:
If the challenge was "don't pick a goat", you should always switch because there's a 2/3rds chance you picked a goat the first time
Click to expand...

What makes it so bizarre is that if another person walks up now, having missed the preceding, they are faced with two doors, one of which has a goat, one of which has a car. They pick at random and for them the odds are 50:50. If they switch there is no logical difference between having picked the other door in the first place. But the original person standing next to him who equally doesn't know which door hides the car (or doesn't have the goat), can make the switch and have different odds.

Now the trick is presumably that the original person has information that the late arrival does not. So because it's probability, they are different scenarios. But you have two people who picked door A, changed their minds and went for door B. But one has a greater probability of finding a car than the other. They're actually different scenarios but I think the unintuitiveness comes from thinking they're the same.
 
Overly Serious said:
Now the trick is presumably that the original person has information that the late arrival does not. So because it's probability, they are different scenarios. But you have two people who picked door A, changed their minds and went for door B. But one has a greater probability of finding a car than the other. They're actually different scenarios but I think the unintuitiveness comes from thinking they're the same.
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Probability calculations are always defined by the exact information someone has, otherwise all probabilities would be either 0 or 1.
 
Overly Serious said:
Anyone else find this throws them for a loop? If so, why? If not, also why? The maths is trivial. I have no problem following it. But the implications are bizarre. It's a kind of mental illusion where you appear to have the same event described differently by two contradictory mathematical models, implying that maths is aware of past events. But the awareness is on the part of the person not the maths, that's the illusion.
Click to expand...
It's one of those things that caused me an issue at first, and I actually had to think a while to get over it. It's maybe a smarter person's version of the "how would you feel if you didn't have breakfast" meme. Once you do, though, it's easy, and it makes a lot of other things make more sense, too.

If you have ever done gambling PvP for profit, like poker, a lot of the profit is in people literally refusing to even understand Bayesian logic (although like you point out a frequentist approach gets you to exactly the same result).

It's almost insane if you ever try to explain the Monty Hall "paradox" (which isn't) to someone who literally can't grasp it. Or worse, and possibly even dumber when it's a person who COULD grasp it, when they absolutely refuse to understand it.

It's also hilarious if they actually get mad while being totally wrong. I used to post variants of Monty Haul to 4chan and it would instantly ignite a huge thread of idiots arguing about it, being right, being wrong, trolling and pretending to be wrong, etc.

And I like you actually did a Monte Carlo simulation of it. It's the sort of thing that makes it absolutely clear that it's true, but then you have to think "why?"

THE MOAR YOU KNOW the better your luck is.
 
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