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she is the only woman in the world who achieved that medal you can do a research on internet about it

Have you read Neil Levy's work on this topic?

really great talk again, great history. I'm still pretty new to this and biased because I learned from Eric's material first, however... There's lots of stuff in history, "arbitrary choices" as you would put it, that ossify and set in stone as convention unless they are quickly overturned. And so even if there is a small but compelling reason to arbitrate differently, it's worth considering, especially in a field so (dare I say) young. For some examples... qwerty keyboards. Maybe back in the day they couldn't have the foresight to predict dvorak or other formats would have some marginal advantages. You can very well argue "we'd all be better off if the better convention took root". But how much better off? only a marginal bit. And people today can still customize their keyboards as individuals if they prefer. And yes that customized keyboard won't be easier for others to immediately pick up. But it is what it is. Then there's driving on the left vs right side of the road. Why does it have to be different? idk. But it's not the end of the world. Just have to know which territory you're in and which rules apply. Would it be nicer if everywhere followed the same convention? sure. Anyway all that to say.... Personally, I like Eric's arbitration. I think the grade of the object matching the shape itself makes a lot of sense. If taking the wedge increases grade, and performing a join adds dimensionality of the objects, it's only reasonable that joins should be the wedge (and meets should be anti-wedge). You say it was completely arbitrary. And to some extent, you're right. It's all opinion and preference at the end of the day. But it's exactly in that way that I say my opinion and preference is Eric's approach. So which convention would be better for everyone to adopt? or rather what should we teach to new people? For every point of conflict Eric's approach has with other dialects of PGA, I think it gains just as many points for staying closer to Vanilla GA. Increasing grade = Increasing dimensionality. In the bottom left corner of the video I see the e1 e2 e3 as planes without orientation arrows and e31 e23 e12 as lines with spinny arrows. It feels wrong. Aesthetics is one of the appeals of GA. Everything changed when I realized rotations happen in planes (bivectors), not around axes (vectors (univectors, sorry lol)). Not staying true to that feels like a step backward, or as Eric might put it, a hack. Anyway. Again, there's no reason we can't all get along and translate between conventions with a little extra work. But if there is a conversation or hypothetical wishful thinking about "if only we had one convention instead", then my vote is in Eric's formulation. Apologies if I made any mistakes or miscomprehensions. No grief intended. These things just take time to digest.

this is an amazing atlas thank you so much

Fantastic talk with lots of lore. Great history for people born into GA like me instead of a conventional LA/matrix background

31:45 absolutely love your description of cross products. Like programming in a language without types - "it's so easy to learn!" but the truth is you are not escaping types, you are just exclusively using the "Any" or "Object" type and not doing your future self many favors

Here's the game that takes place in elliptic space! store.steampowered.com/app/485680/sphereFACE/

Lol

I can just imagine 4 dimensional beings just looking down on 3 dimensional beings talkign about them like fish.

I fidn the mask distracing

روحت شاد مریم بانو خیلی حیف شدی🥀

Thank you

In this representation it could be worth mentioning that 4 dimensions enable two simultaneous but independent rotations, one along one 2D coordinate plane and the other along the plane of the remaining 2 dimensions. Thus there are no "axes" of rotation but rather planes. Considering the 3D surface of the 4D sphere, longitudes and latitudes could also work better if we visualize them as a grid of cells made of intersecting surfaces rather than lines. The system (or one of the possible systems) would have two orthogonal "equators" lined with prism-shaped cells while all the other cells are distorted cubes.

Rotations in n dims = n C 2 (n choose 2)

great video, however it was infuriating hearing how you pronounce geodesic lmao

Is there any evidence of higher spacial dimensions in our universe?

I am inspired . Thank you for making this video. ☺☺

Why mention anything about her religion most Iranians don’t even practice the religion they just have to role with it cuz of the government hence the headscarf when she was living in Iran. Would’ve preferred if you just focused on her great talent.

This is the best explanation I've seen!

By coincidence i have just taken i look of a picture of Clifford's grave in wikipedia

I agree with you that Clifford's algebra is revolutionizing the world

I guess The number of rotational degrees of freedom would be n*(n-1)/2 which is equal to the sum of k with k varying from 1 to n, with step 1.

She was not Muslim not all people in Iran are Muslim. The Muslim and not Muslim were forced to bare hejab. But as you evidence seen the last 2 years iranain women ones again find thier own positions in this crazy terorist cuntry of Islamic repoblic of terorist and shown they are against terorist and all also not fan on Islam regardless of any kind of 76 kind of Islam. So you don't need to call he Muslim

The “number degrees of freedom” of rotation, is referring to the dimensionality of the rotation group, right? So, in 2D, the group is SO(2) (the circle group), and in 3D it is SO(3), and in n-D, SO(n) an element of SO(n) is specified by giving an ordered orthonormal basis of n-D space (such that the determinant you get is 1 rather than -1, but that requirement won’t change the dimensionality) specifying the first vector, there’s an n-1 dimensional choice there (the minus one is because the vector has to be of a specified length, so we remove a factor that is from scaling), and then the what remains is to pick an orthonormal basis for the subspace orthogonal to the vector chosen first. So, f(n) = (n-1) + f(n-1) And f(0)=0 so, f(1) = 0, f(2)=1, f(3)=3, f(4)=6, Yeah, these are the triangular numbers, so, the dimensionality of SO(n) is n(n-1)/2 . So, in particular, the dimensionality of SO(5) is 10.

enjoyed so much watching your stream! where can I watch your lectures? I want to learn more about this Geometric Algebra, it sounds awesome! And is there any resource that I can read or listen to ?

This was interesting, thanks for uploading

1, 3, 6, 10, 15, 21, 28, 36..........?

Awesome video. Very valuable information! Just wondering. To which extend have you explored Buddhism? The core of Buddhism, as a praxeology - not a religion, is that of a handbook on meditation. And depending on the branch, you might find different interpretations of the virtues (patience, compassion etc.) to go along with the meditation. But surely, you're not saying that meditation is virtue signalling? I mean, it could be, "Look at me, I can meditate for 2 hours. What's your record?" But for the most part it's a private process - one of the few things that we DON'T project on to the whole world. So where do you draw the line between useful things coupled with a genuine desire to share them with other people - and pointless bragging that might occasionally lead to scientific breakthroughs?

Super elegant explanation!

I suck at even remembering most of the math in high school. What are the minimum concepts i need to relearn to be able to properly learn geometric algebra? Thank you.

The number of degrees of freedom is n choose 2 because rotation happens in 2 out of the n dimensions.

Nice, but that's not what I was looking for. It's said that a 4d creature can mirror 3d objects, so I'm looking for a computer animation that shows how that would look to us.

Maryam...🇮🇷🇮🇷🇮🇷🇦🇿🇦🇿🇦🇿👏👏👏

Thank you hamish

I love the fish so cute

Let's et one thing straight. There are strings of women in history who deserved way more than the field freaking medal. bUt of course, as always it is an old white creepy guy game only. Cause Katherine Johnson would have deserved two in a row.

Gosh no she was not a muslim. 😤We Iranian woman are forced to wear hijab and be muslims we never chose it. If an Iranian woman leaves Iran and still has their hijab on it means they are probably a believer in Islam or they are so used to it they need more time to decide. If they don’t wear it anymore it means they never wanted to and they were forced to do so their entire lives. Man I’m so sick of religion oppression it breaks my heart to see that not even injustice about Maryam is acknowledged who’s going to acknowledge our’s?!

Bad explanation, so many bloops. Also maryam was the first and only woman to win the filds and no where is mentioned she is muslim. Not just beacuse she is from iran, she is muslim. There are so many people from iran who are NOT muslim.

Woo yeah 👏

Fugitive brains from the Nazis of the Islamic regime....Maryam Mirza Khani, your soul is happy

The rule is (n)(n+1)/2

Maryam Mirzakhani was not a Muslim, she was an atheist.

It's interesting that the shadow of a 4 Dimensional Sphere, looks very much like the magnetic field.

Thinky

So boring...

She was not muslim😡 We Iranians are Forced to be Muslim 😡

Time is our broken perception of the 4th dimension. We here (living in a 3D experience) can’t perceive the entirety of 4D reality, so we break it down into 3D phenomena that change over time. So, time literally is the 4th spatial dimension, but spread out as a temporal experience. Time is the point where 3D intersects with a 4D object.

2:20 The projection of the sphere’s shadow onto the 2D plane is identical to the Steinmetz diagram of electromagnetism. Apollonian circles, each pair of which meets at 90 degrees to one another, ie like being inside a torus. This is also what the Yin Yang symbol means. It’s a symbolic representation of a 4D sphere, or a 3D torus, as a 2D image.

Reason I came here is to understand this better... when a hyper cube is rotated it looks like it's propagating ... so I got to thinking what does a sphere look like spinning.. does it also look like it propergates like a hypercube the I remembered the two ways you can rotate a hypercube and realised its not two ways but the combination of both or it would would not be rotation. I'm beginning to think that light lies on the boundary of two and 3 dimensional space and black holes are onthe boundary of 3 and 4th dimensional space and the rotation of an atom is 4th dimentional