What is a Vampire Matrix?
ฝัง
- เผยแพร่เมื่อ 22 ก.ค. 2024
- Apply for a paid internship at Jane Street! Or, a job.
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Vampire Numbers on Numberphile with James Grime.
• Vampire Numbers - Numb...
Flammable Math's original tweet:
/ 1306303462607654914
Robin Houston gets involved:
/ 1306539901576503297
Here comes Greg Egan!
/ 1306565923671736320
Robin's tweets about characteristic polynomials and the Cayley-Hamilton theorem. I suggested looking them up and working through the logic yourself. It's straight-forward enough and good fun.
/ 1306588415001915393
Robin's code for finding 2 × 2 examples:
gist.github.com/robinhouston/...
Robin's 3 × 3 monsters. If you can beat them: let us know!
gist.github.com/robinhouston/...
My previous video about log(1+2+3)
• What's the story with ...
Behold the pi matrix which squares to give more pi!
[[15,143],[52,936]]
www.wolframalpha.com/input/?i...
CORRECTIONS
- At 07:20 I say 81 when I mean 82. The on-screen number is correct.
- I accidentally say "log troll" instead of "division troll" at 03:38.
- At 03:45 I cross out the wrong 7. Whoops. Gives 117 instead of 171. First spotted by Ryan Parker (no relation).
- I think that's all. Let me know if you spot any more mistakes.
As always: thanks to Jane Street who support my channel. They're amazing.
www.janestreet.com/
And thanks to all my Patreon legends. Your support paid for that cape. Let me know if you have any other video ideas I can use it for.
/ standupmaths
Spoooky wardrobe, make-up, filming and editing by Alex Genn-Bash
Spoooky maths animations by Matt Parker
Extra-spoooky music by Howard Carter
Largely non-spooky design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/products/5b9f...
Nerdy maths toys: mathsgear.co.uk/ - บันเทิง
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Stand up maths: where every thing ever related to maths always circles back to pi
"circles back to pi"
I see what you did there
But surely you are thinking of Tau?
Did you know 1=pi/pi?
Haha circles
Are you forgetting about the golden ratio sir?!
Nobody:
Mathematicians: “Let’s spend hours of our lives and apply linear algebra to troll people!”
🤣🤣👏🏼👏🏼👏🏼
Math is love, math is life.
@@torlumnitor8230 yep
Bruno Belotti yeah like string theory, (the only thing is that people don’t see their applications in “real” life)
😂😂😂
MATH problems
Best Integral question
th-cam.com/video/Wc-U1OPdKJc/w-d-xo.html
See one time.
From now on, any time I want to do something but worry I'll be too embarrassed, I'll remember that Matt Parker turned himself into a fractal Dracula and proudly declared "I'm Fracula!".
If Matt can find the bravery to do that, we all can find the bravery to do anything.
Life if for taking risks! (On every scale.)
Life is for taking risks! (On every scale.)
@@standupmaths Such as posting a public comment before proof-reading it? - Oh! I see what you did there :D
Just give it a go. It may end up just as awesome as Fracula :)
@@wite6509 One can only dream...
Transforming into a calculator is a really bad ability, at least the bat thing gives you extra mobility, but a calculator? What does that give you? Floating point errors?
Could be worse. Could've been a solar powered calculator.
Is it a calculator that tends to express rational fractions as a function of pi?
@@pembrokeshiredan 😂 solar powered calculators are the natural nemesis vampires
I suppose you could call it a ‘Parker Transformation’.
On the plus side, since vampires hang upside down (or perhaps I should say umop apisdn), his calculator's 5318008 will be the right way up.
Honestly, I'm most impressed that you can talk so well with fake fangs. You don't sound any different than normal.
...wait a minute
O H N O
Ahahahaha 😂
I'm questioning whether he had trouble with k's or if "Fangs to Jane Street" was a pun
That's cos he's anti ... Antipodean!
Have we ever seen him eat garlic?
Look out, Fracula! You almost touched the silver ratio
Silver is for werewolves. Fracula has to avoid the cross product
@@kdc-wy3su Vampires too! They can't see themselves in the mirror because mirrors have (had, actually) a silver coating, for example. (I mean, both don't exist, but it is in the folklore that silver hurt vampires)
@@astropgn Mirrors do exist tho...
@@kdc-wy3su wins the thread. :D
@@benjaminmiller3620 I think he meant that vampires and werewolves don't exist.
Also, wasn't silver like really deadly to the undead?
My favorite is X² = 25. The 2's cancel... So... X = 5
I don't get it...
@@raulgalets The two from the exponent and the two from the 25 go away and you get X=5. Does that help?
What about e^2ln(5). The e and ln cancel and you get 25
Sadly, that is just 50% right xD
yeet conjecture intensifies
"This is not going to get too silly." "Before we get too vampirey though.." *proceeds to gradually get too vampirey*
Omg, I got scared at the end at 11:40.
"Hehehe totally worth it!"
As another youtuber would say in the field: "and that's a good place to stop". :)
@ , OK, great.
blackpenredpen, my favourite quote from you is "I don't like to be on the bottom, I should be on top".
thx for the warning, bprp
"They did the Maths, the Monster Maths!
The Monster Maths, it wasn't done by halfs!
The Monster Maths, it gave them ghostly laughs!
The Monster Maths, they did the Monster Maths!"
Kind of expected 196,883 likes on your Monster of a comment.
@Bob Trenwith math ~> mash
maths ~> mashes
It was a graveyard graph!
@Bob Trenwith
maths = mathematics
Math = mathematic???
@@nickwilson3499
Math(ematics)
Math.
I find it amusing that the clip Matt showed of James Grime looked more vampiric than Matt did by the end of the video
Ya !! He appeared so pale!
some hate on white ppl for being too white and hence sickly/ vampiric... but it's politically incorrect to comment on someone being too black. hmm
that's cuz calling someone white is a compliment, not an insult, lol
@@DNXTMaster wait what? How can a color be insult or a compliment? It's just a color, either it's someone black or he's white, there's nothing to be insulted or complimented upon. Some people like to stay white, some like to get tanned, beauty is relative.
@@DNXTMaster how? As I just pointed out, being called white/ pale is often a criticism.
My favorite math troll, is the one feautred in mathloger's video on fermat's last theroem. It goes like this:
3 ^ 2 + 4 ^ 2 = 5 ^ 2
3 ^ 3 + 4 ^ 3 + 5 ^ 3 = 6 ^ 3
but the pattern then stops there.
If the pattern had continued, it would probably have been my favorite theroem in math.
That is pretty neat. It reminds me of this one, not sure if you find it interesting at all:
(1 + 2 + 3 + 4)^2 = 1^3 + 2^3 + 3^3 + 4^3
This pattern actually does continue.
I love how you're always coming up with new version of the channel theme music
It's only the second time now. Unless I missed something?
@@MB-ny6is this version, the orchestral version in the Land Area video, and the piano version on the Superpermitations video, that's at least 3
the orchestral one: th-cam.com/video/PtKhbbcc1Rc/w-d-xo.html
the piano one: th-cam.com/video/_tpNuulTeSQ/w-d-xo.html
halloween: 11:49
Just makes me want to put his music in my playlist more and more
We need the spooky version uploaded asap!!
Your method of reducing fractions is a preferred method of my fifth grade students. They find having to use a common factor too much work and love to just random cancel out numbers. They're not usually so concerned about it yielding the correct answer, though. They get very annoyed when I make them actually find the correct answer.
I was so sure that Troll Maths were going to be based on the "One, Two, Many, Lots" number system of the silicon-based trolls on the Discworld
"Many many" comes before "Lots."
@@FahlmanCascade Thanks, I obviously dropped out before we got to that level of complexity.
Step lots: cover yourself in oil
@@FahlmanCascade Lots comes after "many, many, many, many" - trolls being only able to count in base 4... cos that's how many digits they have on 1 hand
Correction: the wrong 7 is crossed out at 3:45 to produce the same number, causing it to end in 117, not 171.
I noticed too, luckily there's another 7 there lol
Whoops! I’ve added you to the corrections. Thanks!
@@standupmaths It's just a Parker vampire number
Darn it! I knew I should've dug deeper in the comments before saying the same thing
@@user-rv9vk8by5i Same
I thought the calculator would have displayed « LOW BAT »
I was expecting it to flash 800 ("Boo") at the end.
"10:35 I wanna say fangs to Jane Street"
*My Immortal intensifies*
MATH problems
Best Integral question
th-cam.com/video/Wc-U1OPdKJc/w-d-xo.html
See one time.
7:18 "41*2=81" That's some stand-up parker maths right there!
"Pseudo Vampire Number"
so.... a Parker Vampire Number?
Fun fact: my absolute hatred of the tedium of manual matrix multiplication in highschool and uni inspired me to drop maths and physics and lead me into a career in medicine. Now I spend most of my spare time hating my job and watching maths/physics/rocketry videos wondering what might have been. Fun times.
At the very end. Was that Calcula?
Fracula, he said.
Yes, but after that he transforms into a calculator.
Indeed! But I fear it was out of BAT-ary
Better than turning into calculas
Better than Flatula.
Therapist: Fracula doesnt exist, he cant hurt you
Fracula:
It's probably an irrational fear.
I watched this channel for years and every video the quality improves, the theme music changes and I just get the biggest smile on my face every time I watch a video. Thank you so much Matt for every video you put out
"But then, Greg Egan joined the chat."
You mean the science fiction author?!
"Greg is the science fiction author"
WHOA
This is the best substitute to trick-or-treating.
In fact, it's a bonus, because I never went trick-or-treating even before lockdown.
I never went trick-or-treating either, but I miss having the choice.
10 minutes that felt like seconds, the greatest content around! Keep going, its a lot of fun watching you! Thanks for all the work!
This video is an outstanding video, even for this outstanding channel. You have outdone yourself here. I deeply appreciate this topic and the production gone into this. Please keep this up and keep inspiring!
There are 408 instances of 3x3 vampire matrices of single digit (non-zero) numbers. Several of them are re-orderings of the same rows/columns and many have repeated digits.
Some nice ones (little repetition) are:
[2 3 6] [5 3 3] [25 33 63]
[2 2 7] x [3 7 1] = [23 27 71]
[3 4 4] [1 1 9] [31 41 49]
[2 7 6] [7 1 9] [27 71 69]
[4 4 9] x [1 9 3] = [41 49 93]
[1 2 2] [1 1 5] [11 21 25]
[3 5 4] [4 1 9] [34 51 49]
[4 4 6] x [2 8 2] = [42 48 62]
[2 3 3] [3 2 3] [23 32 33]
Awesomely fun and creative! You are a by-gosh spellbinder! "Yes, Maths-ter, I am your faithful servant, coming, coming..."
Always love hearing Greg Egan did more crazy stuff. Dude wrote my favorite book ever "Diaspora". It's awesome hearing about him popping up in other things I love like your videos Matt. :3
I just wrote an exam where this characteristic polynomial was a thing.
Exam done, lets go do helloween!
Matt: *spooky matrices*
Love the rotoscoped Matt on black background aesthetic. vey soothing!
Matt Parker switching to a vampire outfit in the middle of a video is now my third favourite moment in the history of mathematics.
Idc what they say your PI one is special!! I love it!! I’m always saying wow when I watch everything you do
Great episode. Love how the costume got subtly more vampiric throughout video.
Me: No way Pi is gonna show up here.
Matt: Hold my beer.
I just want to express my appreciation for your dedication to the vampire theme
Excellent video! Made me laugh out loud when you got to 'and this is how we look for pi'. Thank you for that.
I often cannot understand the maths that MP is explaining (this one of them), but nevertheless I am always fascinated. Loved how he transformed himself throughout the video.
Your music is always so good! I love it
Brilliant video. Really quite the show and sense of humor.
amazing video as usual matt such an inspiration for me when i need to think of video ideas! :)
Absolutely brilliant.
Also this Extra-Spooky music slaps hard!
so you are telling me I can troll ppl with Maths, too... omg, what a superpower I've discovered today
I totally need the piano version of the stand ups math and now, more than ever... The spoooooky version.. Math, be a great guy and release it! :D
7:18 Matt says he multiplies 42 by 2 to get 81, when in fact he gets 82 as the video correctly displays.
Multplying by two today gives you an odd number... SPOOOKY MATHS!!
Especially then the number you're multiplying by is also odd
Hey I just learned the characteristic polynomial in class! That's so neat :)
one of, if not the, best videos you've ever made, congratulations 👏
That cheekbone shadow is very well done.
One day this channel will definitely join "recommended for you channels" club.
Hi fellow Agadmator fan
i love ur last name, Levent
Matt, you are a gem. This is both esoteric and hilarious.
Matt, that outfit [frilly shirt with medal & jacket] looks sooo good on you!
i am not used to this level of editting.
11/10 will watch again
The video was great, but the closing melody... Just awesome
I have heard that Count Von Count's propensity for counting things is inspired by (or probably just coincidentally meshes with) an obscure bit of vampire lore where if you throw a handful of rice or what have you on the floor, the vampire will compulsively count the grains, allowing you time to get away. Which doesn't sound far off from some mathematicians, though they'd devise a method to approximate the number of grains of rice.
The soundtrack is getting better and better
That Pi matrix with which you came up is some niiice matrix.
Entirely unrelated to the interesting maths but the clean shave is definitely looking great my man.
When you say "spooky maths" it reminds me of the guy who played death in Horrible Histories.
Also, I got very distracted by the fangs and how well you talk with them in.
I could not notice the fangs until the whole costume was on
This video is true dedication to the costume bit
Silly Matt at 7:18, 41x2 = 82. On a serious notes, your videos are always amazing haha
Thanks Matt. That was an excellent video and I definitely laughed out loud!
Love everything about this. Great job
Wasn't expecting the good ol' Cayley Hamilton Theorem to come up, SPOOKY MATHS!
I can visually see the effort behind this video!
6:41 I have just passed an exam on linear Algebra and Group Theory and finally I understand what you are talking about :D
The efforts! This man is amazing 👍
You had me at "What we deduce in the Shadows"
Do you want another spooky maths trick?
I call it the Parker Thelepathy:
1. Think about any Integer.
2. Multiply it by a number of digits it has
3. The resulting number's digits are the digits of number Pi. I mean they are not in a correct order, but still...
9:57 It'd be hilarious if that's how we really found more digits for pi. Imagine how fun it'd be to try and order the digits properly!
Love the gradual transformation
I am now double subscribed to your channel!
Too much fun was had in the making of this video
Fracula could be a boss in Delta Rune, easy 0.0
Also, despite the incredible maths on display, the most mind-boggling part of this video is how you managed to not puncture your mouth with them fangs :D
My favorite is Troll Commutativity. 2 + 4 = 4 + 2, therefore addition is commutative. 2 × 4 = 4 × 2, therefore multiplication is commutative. 2⁴ = 4², therefore exponentiation is... wait a second...
I LOVE the spooky remix of the Stand-Up Maths theme song. Seriously, it's awesome.
"Fracula"! OMG! Almost choked on my tea.
wow hey man i really like the way u explained this one :) have a nice day.
All of this linear algebra brings up some real dread in me, very appropriate for Halloween
Vamπre numbers in the last example. I love it!
Matt had way too much fun making this video!
OK, that last joke had me laughing out loud. Worth the maths headache I got trying to keep up. LOL
I love how you slowly got more and more vampirey
Oh jeez this spooky maths was too spooky for me. The maths in spooky maths was spooky and it spooked me with maths
Well done, sir!
I'm totally vamped for spooky maths!
Matt always puts a smile on my face!
Greg Egan + Matt Parker?!
Ive never seen a cross-over event like this yet!
I read his book this year, Diaspora, and it blew my mind to shreds. Did not expect to here his name here, but I guess it's not surprising either :D
Love the fangs! 🧛🏻♂️ That was fun-Happy Halloween! 🎃🤖🤡👹😈👻💀👽🧟♂️🧝♀️
By writing the equation for a general vampire matrix multiplication as AB = bA + B we can reduce the brute forcing requirements considerably: given B we can find A with an inverse and a multiplication, so for 3x3 we just need to handle b^9 instead of b^18 cases. E.g. [[2,1,2],[3,1,5],[4,2,5]][[0,0,5],[8,6,1],[6,2,7]] is a vampire.
The lexicographically earliest (reading A by rows) is [[0, 1, 1], [1, 1, 1], [1, 2, 1]] [[6, 4, 2], [2, 8, 4], [4, 6, 8]]. There are more than 7000 which don't even have any zeroes (a zero in A being kinda cheaty), of which 336 use all of the digits from 1 to 9. The lexicographically earliest of these is [[1, 1, 1], [4, 2, 3], [6, 6, 5]] [[3, 1, 1], [1, 7, 2], [9, 3, 8]].
Oh, Count Fracula! Your bloody math has me swooning.
"What we deduce in the shadows" fantastic!
There are indeed 3x3 vampire matrices with distinct fangs. For example:
[[1, 1, 1] [[1, 1, 1] [[11, 11, 11]
[2, 1, 2] [1, 6, 1] = [21, 16, 21]
[8, 9, 8]] [9, 4, 9]] [89, 94, 89]]
I found a few by brute force, and my algorithm doesn't scale up well, so I don't know if there any with 2 digit numbers
Masker: helps Matt into vampire costume
Matt, half way through: "Thanks, I'm gonna make a video and be back later"
Amazing maths channel.
"We drink your blood and we square your matrices."
Powerwolf...I mean Powermath! :D
You go in a dark forest looking for trolls and you find vampires instead. And then they say math isn't an accurate depiction of reality - if it's good enough for heroic fantasy it's good enough for me!
*hears "fangs" pun being used unironically*
*gets My Immortal flashbacks*
Insert Parker square reference