Hey, I'm Domotro. Welcome to Combo Class! Get ready to learn some crazy things about numbers, nature, language, philosophy, and more!
This is the home of my main youtube series, but also check out my @Domotro channel for all of my shorts, livestreams, and bonus videos.
DISCLAIMER: Do not copy any use of fire, tools, or other science experiments you might see in any Combo Class episodes. Everything in this series was filmed safely and professionally, with the goal of teaching people about mathematics and other educational topics.
I discovered the golden ratio at age 14 by looking for the number with the property 1/x = x-1. I also discovered that if you had a ravigneaux planetary gearset with a ring gear that is the golden ratio times larger than the sun gear (actually, both sun "gears" since there are two of them), you could make a four speed gearbox with ratios of 2.618, 1.618, 1.000, 0.618, and a reverse ratio of -1.618. (side note, I realize you can't make an irrational gear ratio with finite tooth count gears, but either approximate with large numbers or use discs with a high coefficient of friction)
For complex numbers I think the base unit of the cost/complexity has to be i. The series varies wildly based on whether or not we permit subtraction. Without it we start something like 4, 5, 6, 6, 10...
I feel like education should be focused on teaching people to intuit the difference between someone like this and that guy Rogan had on recently... Terrance Howard. How does one know whether someone else understands what they're saying? How does one determine whether they themselves understand what they think they do? Is it possible to teach? Can people *learn* to tell whether someone is genius vs. nut jobs vs. con artists?
the reason it must fall a whole crap ton no matter how much it rises is because of 2 reasons 1: multiplying an odd number by an odd number will always be odd, because if you think about it, odd numbers have an extra piece for another odd number, hence odd+odd is even. When there is an odd number, each of the others get paired up with each other, but there is one more odd, which makes it all in all odd. Adding one will guarantee its even, which will divide by 2. However, since there isn't a guarantee that dividing by 2 will result in an odd, it will always fall more than it rises. Its simple, and because it can never rise more than it falls, there isn't another loop outside of 4-2-1. Its simple??? and 2: what goes up must come down.
Is scary how confident is chatgpt at lying and saying general nonsense. And even scarier that some coworkers use it daily and take it's output as gospel.
Question: is there ever a power of 2 which you can construct strictly more efficiently than repeated (1+1)? In theory, if we have a power of 3 that's sufficiently close, the increased efficiency of the 3s could save enough 1s to make up for the imprecision. Sounds hard; Is your instinct yes or no, and how long do you think it would take to prove?
I wonder if this can be used to store numerical information in computer code strings, cleverly manipulate those strings for each calculation made, and then evaluate and convert everything at the end from binary to decimal! It sounds like extra steps, but it could be more efficient since it would be fewer operations overall.
*This* is what the internet is for in the area of math, just putting out there ideas & concepts you have encountered/thought of and hopefully eventually someone will find it and can think on it, give a new set of eyes. We can advance with mostly unheard of or new ideas that no one would have really taken the time to dive into, that would have been forgotten otherwise. Occasionally, inevitably someone will think of something new. Instead of forgetting about these things and just going “huh. Whatever.”, *document it* in some way. Even just write it down in a notes app or something, but preferably in a way that will make other people think about it.
i dont know if you have cracker barrels where youre from, but at cracker barrel every table has this peg solitaire game thats quite tricky. i could never beat it as a kid. you can actually equate it to a group structure and use abstract algebra to show which moves lose
Why do I have a feeling that whenever I watch videos from this channel some hungry people will be talking about 20th of April? BTW. Thanks for the video.
It seems complicated to people, but imo using patterns is infinitely more easy than rote memorization of the entire table. In fact, it blows my mind that people actually do that. I actually didn't even learn with a table. I just gradually picked up on various patterns myself as I progressed through math. Idk why, but my school didn't even use times tables for the gifted class. Only the regular class was forced to memorize them. I guess they just assumed we'd pick it up naturally? They were right, but I think most people really don't even need the table to get good at it.
Missed opportunity to share a very nice fact: the only number in base 10 (or any known base) whose square and cube are together pandigital in that base is 69.
This feels tailor-made for people with ADHD. There's never a moment to get bored because there's always something new on screen to pay attention to while listening.
the part about the positional numeral systems being equal to the base to incremental powers reminded me of the standard notation of polynomials with a single variable and now im interested in the connection between polynomials and numeral bases, and extrapolating from that the connection between logarithms and numeral bases. im sure theres a connection between e / natural logs and numeral systems by way of this property. ill have to work it out. very cool stuff
There is a widespread misconception about the aleph numbers. It is known that the cardinality of the real numbers is the same as 2^(Aleph_0). Cantor himself proved this. The Continuum Hypothesis is the claim that Aleph_1 = 2^(Aleph_0). This is the statement which is independent from the standard axioms of set theory, so we can't say that it is true, and we can't say that it is false. But the misconception is what Aleph_1 means and what 2^(Aleph_0) means. By definition, Aleph_1 is the smallest cardinal number greater than Aleph_0. And by definition, 2^(Aleph_0) is the size of the power set of the natural numbers. But the popular misconception is that these things have the opposite meaning. It is commonly _wrongly_ believed that Aleph_1 is, by definition, the cardinality of the set of real numbers, and 2^(Aleph_0) is the next cardinality after Aleph_0. But again, those are _wrong_ and got popularized for some reason. Apparently, there was an old book that _assumed_ the continuum hypothesis (without saying that it was assuming it) and caused the widespread misconception.
The "double or add 1" version was used in an old game called "Wizkid" as kind of a cheat code. You would walk through different doors to reach your target number
These kind of loops also happen in YuGiOh, in fact the official konami documentation mentions "infinite loops" and gives an example with a card called Pole Position. In this case if the loop does not eventually cause a victory condition, a judge determines what's the problem card and sends it to the graveyard so the game can continue.
Your mind seems wildly tempered in wonderful ways, I would love to sit down and talk shop about large number theory and complex relative maths. The video was a wild ride and is worth recommending to a friend.
Additively I'd like to give you another indexing idea that I think will lead to the future of number theory, if Pi is infinite we could theoretically have all numbers derived from Pi and using either their integer value to return different values (0 gives 3, 1 gives 1, 2 gives 4 but say 0~2 would be 14) to eventually have computers look at all numbers as their related index of pi, depth of relation of numbers and since it goes on indefinitely you could get all values eventually when they are all tallied.
Kiwi peel is genuinely good. It adds a lot of flavor to the fruit and is very soft compared to other peels. When I found about it about 5 years ago, I felt bad for all the kiwis I ate the wrong way.
