notch

you’ll get mad at me for saying this…but cloud gaming is so obviously more economically efficient than physical hardware I think it’s going to be the default soon. your home console / pc is idle 90%+ of the day. meanwhile, data centers targets what, 5%, maybe at worst 10% idle. every second a cloud gamer isn’t gaming, that hardware is being used for someone else, training, etc. I think there should be a new measurement, something like cost-per effective FLOP hour that takes into account the TCO + effective utilization. If a gamer spends $500 on a GPU, uses it for 3 years, but it’s only fully active ~5% of that period…the cost-per relative FLOP hour is crazy high! Meanwhile, a $50,000 datacenter GPU might have a *LOWER* cost-per FLOP hour just because the effective utilization is 90+%.

you’ll get mad at me for saying this…but cloud gaming is so obviously more economically efficient than physical hardware I think it’s going to be the default soon. your home console / pc is idle 90%+ of the day. meanwhile, data centers targets what, 5%, maybe at worst 10% idle. every second a cloud gamer isn’t gaming, that hardware is being used for someone else, training, etc. I think there should be a new measurement, something like cost-per effective FLOP hour that takes into account the TCO + effective utilization. If a gamer spends $500 on a GPU, uses it for 3 years, but it’s only fully active ~5% of that period…the cost-per relative FLOP hour is crazy high! Meanwhile, a $50,000 datacenter GPU might have a *LOWER* cost-per FLOP hour just because the effective utilization is 90+%.

We can easily derive quaternions and the Clifford Algebras by defining a geometric product as the sum of two vectors' dot and outer products. We find that by doing this, parallel vectors yield just their dot product when multiplied, while perpendicular vectors are irreducible. If a vector v is the sum of perpendicular unit vectors e1 and e2 then the following must be true: v = e1 + e2 vv = (e1 + e2)(e1 + e2) vv = e1e1 + e1e2 + e2e1 + e2e2 We must be careful how we represent the above because the vectors non-commutative: the ordering of their products does matter as we are representing geometric objects in space, not scalars. Because unit vectors are parallel to themselves: e1e1 = 1 and e2e2=1 Therefore: vv = 2 + e1e2 + e2e1 How do we find the magnitude of vv? We simply use the Pythagorean theorem as e1 and e2 are perpendicular unit vectors. vv = e1e1 + e2e2 = 1 + 1 = 2 Substituting back into our equation previously: 2 = 2 + e1e2+ e2e1 0 = e1e2 + e2e1 e1e2 = -e2e1 Therefore, reversing a perpendicular product yields its negative. This is a core identity in geometric algebra. We can now show a surprising result: imaginary numbers emerge from the algebra we have constructed. To do this, we can consider what happens when we take our original perpendicular unit vectors e1 e2 and multiply them together, twice. We go through our identities: (e1e2)² = e1e2e1e2 = -e1e1e2e2 The last equivalence is true because we simply swap a product with its reverse while applying the negative -- what we just proved previously. The rest is collapsing the product of the same vectors into their magnitude of 1: (e1e2)² = -1 Remind you of anything? Let's substitute e1e2 with i: i² = -1 Therefore, what we we call an imaginary number is equivalent to a bivector in geometric algebra. We have shown that these vectors, when multiplied using our geometric product defined in the very beginning, produces the complex ring. Deriving the full quaternion identity is left as an exercise to the reader. Hint: the lever for increasing our space's dimensionality is in the number of perpendicular unit vectors we define (e1, e2...)