Welcome under Another Roof, where there is always another proof. Videos about mathematics, mathematical logic, and the history of mathematics. Did I mention I like mathematics?
All basis of modern mathematics don't consider 1 as prime, as for 0, its properties diverge from the ones of any other number (except 0, also having some weird properties, and sometimes considered as prime, depending on the context), and is the "base brick" for set theoriy, as S(0) [yes, 0 again, maybe 0 is the base brick for the theory of everything else ?]
@erickleinwolterink35244 сағат бұрын
Imagine if, as a kid, at your second level of education you were first introduced to the concept of numbers in general, rather than a series of functions and lists to memorize... The line of thinking lends itself to learning math in more than one base. Like if binary was taught as well as decimal, much the same as Spanish and English are often taught alongside one another.
@anthonycannet13059 сағат бұрын
9:29 should’ve called it the N dragons problem because the king+rook is the same way a dragon in Shogi moves. In Shogi, the way pieces promote is different. Each piece promotes to a specific other piece, and most pieces can promote. If you move the rook to a promotion square, it promotes to a dragon which can move like a rook but also 1 space diagonally, which is a king+rook so we can just call it a dragon. Similarly the bishop’s promotion is the horse (different from the knight) which moves like a king+bishop
@chrishughes818819 сағат бұрын
Rrecommendation: a link in your tablf of contents to your successor definition. I came back here from episode 3 looking for it.
@SittaCarolinensis19 сағат бұрын
I never quite get the point of this - it would only be really clever if ALL the numbers had to be used.
@chrishughes818819 сағат бұрын
At 12:55, it seems to me like you skipped some reasoning. n + P(k + 1) + 1 equals n + P(S(k)) + 1 which will simplify to n + k + 1 which equals n + S(k) ... But how did you get from here to S(n + k) ?
@AnotherRoof14 сағат бұрын
@@chrishughes8188 informally: Go from where you say "which will simplify to n+k+1" but put brackets here: (n+k)+1 which is S(n+k). All this is just a bit of motivation for where the definition of addition comes from, but hopefully that helps!
@YT2go4meКүн бұрын
Great video.
@ignacio3985Күн бұрын
Really cool video, thoruoghly enjoyed it. I've been thinking about this issue, however I found that logician Jaakko Hintikka made an interesting reconstruction of "the Holmesian sense of deduction" amidst his broader proposition for a "logic of discovery". If I can find his papers again, I'll post them in the reply.
@arden-chanКүн бұрын
I find it quite demeaning when mathematicians and theoreticians say “I leave it as a simple exercise to the reader”.
@cmyk8964Күн бұрын
It seems like if you dig deep enough at any part of math we chance upon Archimedes, Euler, or Gauss
@michaelallen14322 күн бұрын
Holy crap, teenagers DO know everything. The real knees here is that they did something practical with it rather than just arguing with their parents.
@nic123442 күн бұрын
Someone please send this video to Terrence Howard!
@alexanderskladovski2 күн бұрын
This video is exhaustively long. I think you should spend less time explaining the same thing over and over again, because if the audience would've required a more detailed explanation, it would've been ignorant enough to not care.
@hervevazeilles37902 күн бұрын
It is not a British game show at it runs for way more years in other countries.
@hervevazeilles37902 күн бұрын
If we are outside of the UK we are familiar with the original game show. Countdown is just the British version of a French game show that was also adapted in 16 other countries including the USA and Australia Italie or Turkey. It was all around the world before it was imported to the UK.
@AnotherRoof2 күн бұрын
@@hervevazeilles3790 feel like I should turn this into a drinking game at this point 😅
@beebee_01362 күн бұрын
For those who want to follow up on this subject, you may refer to an introductory text on logic by authors like Gensler, HJ. Hope this helps : )
@zachrodan75432 күн бұрын
Another way to justify nC0=1 is that nCk could be interpreted as Given a set with n elements, how many subsets are there with k elements. Every set has the empty set as a subset, and since a set is only defined by its elements, there is exactly one empty subset.
@wiener_process2 күн бұрын
I mean, this isn't that revolutionary, last time I talked to an AI, it managed to prove that the Lebesgue measure isn't countably additive. Now that's a result that will change math.
@lforlight3 күн бұрын
The bricks remaining in frame, representing the accumulated knowledge, are really good. It's like keeping frequently used tools on the workbench instead of on the shelf.
@AnotherRoof3 күн бұрын
@@lforlight they've become a staple of my channel!
@tabassumsultana20153 күн бұрын
3 is the successor of the successor of THE unit.
@DidierPilon3 күн бұрын
(125-8)*5-(6/2)
@matthewfelgate3 күн бұрын
This is the best video I have seen in a long time. I didn't know there was so much to unpack from the Countdown numbers round. Thank you for this video.
@j0hner3 күн бұрын
also if you use a standard 32bit integer on the big multiplication the machine will break so im not betting my life
@j0hner3 күн бұрын
the cake is a lie!
@JohnJohnson-zq9rg3 күн бұрын
I do not like the way you present. To much and to fast talking. Would be much clearer by just slowly drawing and show each step slowly. All the talking about obvious things distracts from the matter. And you are cheating with the protractor. So from that moment i lost interest. Other video's explain the matter much better.
@johnydl3 күн бұрын
2x6=12, 75-12=63, 63/9=7, 8-7=1, 100*1=100... if the numbers round is too easy I have to use all 6 numbers to get there :D
@charlesrockafellor42004 күн бұрын
*Thank you, @AnotherRoof!* ❤ Somehow, the visual at 31:26 (much like many others showing the sporadic symmetry groups' connections) clicked for me when you pointed to Conway, and I finally remembered a book title that I'd been trying to cough up for the past... ~10 years now (for the DIM 26 Lorentzian space → DIM 24 Euclidean [esp. pp. 223-224], re. Leech lattice [now if only I could remember the connection to an arXiv paper re. orbifolds]): “Symmetry And The Monster: One Of The Greatest Quests Of Mathematics” (and all that I had been able to come up with prior to this was “Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics”, re. E7 and E8, understandably).
@rianczer5 күн бұрын
Don't be so quick to dismiss what you see as nothing more than horoscope… nor should you underestimate the ancients' wisdom. The mathematical rigor of academic maths may be reconciled with the esoteric numerology on which people of as enduring intellect as Pythagoras, Plotinus, Iamblychus, and more have reasoned & written. I understand there is a lot of quackery, but a responsible sceptic doesn't dismiss that which he has not understood. "No empirical grounding according to 20th century understandings of the scientific method" is, ultimately, quite a finite criticism. Anyway I don't mean my only comment to be critical. I just shared on facebook that your pedagogical clarity & production quality with what I imagine is a shoestring budget is an inspiration for me. I love your videos.
@extra_preparation66145 күн бұрын
100 x 6 =600 -25 575 +5 +2 = 582
@ravnodinson6 күн бұрын
I know I’m not smart, but holy shit this made me realize I am wholly mentally deficient.
@thestrangegreenman6 күн бұрын
I was ripped off by my high school math classes. This is so much more interesting and understandable than the crap they dumped on us... It's like they left all the reasons "why" out of the lessons
@Obi6706 күн бұрын
100x6 =600 600-25= 575 575+5+2= 582
@AbbyCatYear20237 күн бұрын
.
@HugoHabicht127 күн бұрын
What is e*Pi ?
@jeffreymorris17527 күн бұрын
Look. I'm not stupid. Okay maybe a bit. Anyway, this video of yours has moved me further towards understanding groups than any other video or article I've seen up until now. Still confused af of course, but I've moved into an area of less dense confusion. So good job!
@TheBomber157 күн бұрын
Carol is a brilliant person and a genuinely great mind. She’s sorely missed from Countdown.
@theultimatereductionist75928 күн бұрын
You just flashed Rob Curtis on the screen at 43:12. Who is this Rob Curtis? When did they live? How did Curtis figure out this MOG? Why did he put all this effort into studying just S(5,8,24)? Do similar MOGs exist for other values of t<k<n?
@theultimatereductionist75928 күн бұрын
28:06 PSL(2,7) means "projective special linear"? The S doesn't mean "symplectic", does it?
8 күн бұрын
Loved the intellectual face joke😂
@jakobthomsen15958 күн бұрын
Wonderful 🙂
@leftmit92178 күн бұрын
en.wikipedia.org/wiki/Nikolai_Lobachevsky The man from Kazan.
@jonathanodude66608 күн бұрын
21:33 452 = 9 * 50 +2 ie, very easy.
@donerskine79359 күн бұрын
I skipped to the end because I have to carve up a birthday cake for 17 children in a couple of hours. I had hoped little Jake wouldn't come, he's a horrid little tyke and 16 would have been easier.
@donerskine79359 күн бұрын
You mis-spell 'constructible'. But that's perfictly understandible.
@tolkienfan19729 күн бұрын
Maybe this curve is called The Witch because it has some truly terrible properties. When treated as a distribution, it's mean and variance are undefined! If you encounter it in Physics, you should be very scared. 🤣
@KikeElfísico9 күн бұрын
most incredible and educative video about maths I´ve ever seen
@peyoje9 күн бұрын
Thank you so much for making these group theory videos. Please keep it coming :)
@peyoje9 күн бұрын
What a great video! Finally a video about what I always wanted to learn about. Thank you so much!
@chadnelson89069 күн бұрын
Now explain why 1 set times 1 set equals 1 set instead of 2 sets. 😅
@p0gr9 күн бұрын
it's not cos(20), but cos(20°). it's already terrible for students to confuse these, but more so for a real maths person. you shoud know that the arguments differ by a factor of pi/180.
@AnotherRoof9 күн бұрын
@@p0gr You are technically right. But my experience with "real maths persons" is that when things are obvious from context, you can generally omit them.
@p0gr9 күн бұрын
@@AnotherRoof generally not, if the thing you create by this omission makes sense itself, but a different one.
Пікірлер
All basis of modern mathematics don't consider 1 as prime, as for 0, its properties diverge from the ones of any other number (except 0, also having some weird properties, and sometimes considered as prime, depending on the context), and is the "base brick" for set theoriy, as S(0) [yes, 0 again, maybe 0 is the base brick for the theory of everything else ?]
Imagine if, as a kid, at your second level of education you were first introduced to the concept of numbers in general, rather than a series of functions and lists to memorize... The line of thinking lends itself to learning math in more than one base. Like if binary was taught as well as decimal, much the same as Spanish and English are often taught alongside one another.
9:29 should’ve called it the N dragons problem because the king+rook is the same way a dragon in Shogi moves. In Shogi, the way pieces promote is different. Each piece promotes to a specific other piece, and most pieces can promote. If you move the rook to a promotion square, it promotes to a dragon which can move like a rook but also 1 space diagonally, which is a king+rook so we can just call it a dragon. Similarly the bishop’s promotion is the horse (different from the knight) which moves like a king+bishop
Rrecommendation: a link in your tablf of contents to your successor definition. I came back here from episode 3 looking for it.
I never quite get the point of this - it would only be really clever if ALL the numbers had to be used.
At 12:55, it seems to me like you skipped some reasoning. n + P(k + 1) + 1 equals n + P(S(k)) + 1 which will simplify to n + k + 1 which equals n + S(k) ... But how did you get from here to S(n + k) ?
@@chrishughes8188 informally: Go from where you say "which will simplify to n+k+1" but put brackets here: (n+k)+1 which is S(n+k). All this is just a bit of motivation for where the definition of addition comes from, but hopefully that helps!
Great video.
Really cool video, thoruoghly enjoyed it. I've been thinking about this issue, however I found that logician Jaakko Hintikka made an interesting reconstruction of "the Holmesian sense of deduction" amidst his broader proposition for a "logic of discovery". If I can find his papers again, I'll post them in the reply.
I find it quite demeaning when mathematicians and theoreticians say “I leave it as a simple exercise to the reader”.
It seems like if you dig deep enough at any part of math we chance upon Archimedes, Euler, or Gauss
Holy crap, teenagers DO know everything. The real knees here is that they did something practical with it rather than just arguing with their parents.
Someone please send this video to Terrence Howard!
This video is exhaustively long. I think you should spend less time explaining the same thing over and over again, because if the audience would've required a more detailed explanation, it would've been ignorant enough to not care.
It is not a British game show at it runs for way more years in other countries.
If we are outside of the UK we are familiar with the original game show. Countdown is just the British version of a French game show that was also adapted in 16 other countries including the USA and Australia Italie or Turkey. It was all around the world before it was imported to the UK.
@@hervevazeilles3790 feel like I should turn this into a drinking game at this point 😅
For those who want to follow up on this subject, you may refer to an introductory text on logic by authors like Gensler, HJ. Hope this helps : )
Another way to justify nC0=1 is that nCk could be interpreted as Given a set with n elements, how many subsets are there with k elements. Every set has the empty set as a subset, and since a set is only defined by its elements, there is exactly one empty subset.
I mean, this isn't that revolutionary, last time I talked to an AI, it managed to prove that the Lebesgue measure isn't countably additive. Now that's a result that will change math.
The bricks remaining in frame, representing the accumulated knowledge, are really good. It's like keeping frequently used tools on the workbench instead of on the shelf.
@@lforlight they've become a staple of my channel!
3 is the successor of the successor of THE unit.
(125-8)*5-(6/2)
This is the best video I have seen in a long time. I didn't know there was so much to unpack from the Countdown numbers round. Thank you for this video.
also if you use a standard 32bit integer on the big multiplication the machine will break so im not betting my life
the cake is a lie!
I do not like the way you present. To much and to fast talking. Would be much clearer by just slowly drawing and show each step slowly. All the talking about obvious things distracts from the matter. And you are cheating with the protractor. So from that moment i lost interest. Other video's explain the matter much better.
2x6=12, 75-12=63, 63/9=7, 8-7=1, 100*1=100... if the numbers round is too easy I have to use all 6 numbers to get there :D
*Thank you, @AnotherRoof!* ❤ Somehow, the visual at 31:26 (much like many others showing the sporadic symmetry groups' connections) clicked for me when you pointed to Conway, and I finally remembered a book title that I'd been trying to cough up for the past... ~10 years now (for the DIM 26 Lorentzian space → DIM 24 Euclidean [esp. pp. 223-224], re. Leech lattice [now if only I could remember the connection to an arXiv paper re. orbifolds]): “Symmetry And The Monster: One Of The Greatest Quests Of Mathematics” (and all that I had been able to come up with prior to this was “Moonshine beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics”, re. E7 and E8, understandably).
Don't be so quick to dismiss what you see as nothing more than horoscope… nor should you underestimate the ancients' wisdom. The mathematical rigor of academic maths may be reconciled with the esoteric numerology on which people of as enduring intellect as Pythagoras, Plotinus, Iamblychus, and more have reasoned & written. I understand there is a lot of quackery, but a responsible sceptic doesn't dismiss that which he has not understood. "No empirical grounding according to 20th century understandings of the scientific method" is, ultimately, quite a finite criticism. Anyway I don't mean my only comment to be critical. I just shared on facebook that your pedagogical clarity & production quality with what I imagine is a shoestring budget is an inspiration for me. I love your videos.
100 x 6 =600 -25 575 +5 +2 = 582
I know I’m not smart, but holy shit this made me realize I am wholly mentally deficient.
I was ripped off by my high school math classes. This is so much more interesting and understandable than the crap they dumped on us... It's like they left all the reasons "why" out of the lessons
100x6 =600 600-25= 575 575+5+2= 582
.
What is e*Pi ?
Look. I'm not stupid. Okay maybe a bit. Anyway, this video of yours has moved me further towards understanding groups than any other video or article I've seen up until now. Still confused af of course, but I've moved into an area of less dense confusion. So good job!
Carol is a brilliant person and a genuinely great mind. She’s sorely missed from Countdown.
You just flashed Rob Curtis on the screen at 43:12. Who is this Rob Curtis? When did they live? How did Curtis figure out this MOG? Why did he put all this effort into studying just S(5,8,24)? Do similar MOGs exist for other values of t<k<n?
28:06 PSL(2,7) means "projective special linear"? The S doesn't mean "symplectic", does it?
Loved the intellectual face joke😂
Wonderful 🙂
en.wikipedia.org/wiki/Nikolai_Lobachevsky The man from Kazan.
21:33 452 = 9 * 50 +2 ie, very easy.
I skipped to the end because I have to carve up a birthday cake for 17 children in a couple of hours. I had hoped little Jake wouldn't come, he's a horrid little tyke and 16 would have been easier.
You mis-spell 'constructible'. But that's perfictly understandible.
Maybe this curve is called The Witch because it has some truly terrible properties. When treated as a distribution, it's mean and variance are undefined! If you encounter it in Physics, you should be very scared. 🤣
most incredible and educative video about maths I´ve ever seen
Thank you so much for making these group theory videos. Please keep it coming :)
What a great video! Finally a video about what I always wanted to learn about. Thank you so much!
Now explain why 1 set times 1 set equals 1 set instead of 2 sets. 😅
it's not cos(20), but cos(20°). it's already terrible for students to confuse these, but more so for a real maths person. you shoud know that the arguments differ by a factor of pi/180.
@@p0gr You are technically right. But my experience with "real maths persons" is that when things are obvious from context, you can generally omit them.
@@AnotherRoof generally not, if the thing you create by this omission makes sense itself, but a different one.