Eric Weinstein And The Hopf Fibration

Curt and Carlos discuss Eric Weinstein's theory of everything, Hopf Fibration and mathematics.

NOTE: The perspectives expressed by guests don't necessarily mirror my own. There's a versicolored arrangement of people on TOE, each harboring distinct viewpoints, as part of my endeavor to understand the perspectives that exist.

THANK YOU: To Mike Duffey for your insight, help, and recommendations on this channel.

Support TOE:

Follow TOE:

Join this channel to get access to perks:

#science #ericweinstein

[billschwandt]

Imagine a spring. When you turn with the spring it tightens, when you go against it it flattens. Now imagine a tornado. If you had the tornado by the tail and spun it in circles with the rotation it would tighten the wide part of the tornado like the spring. Finally, imagine a ring like a wedding band laying flat on a table. Imagine the ring starts to wobble around the rim gaining momentum until it stand like a top, then rolls around the other edge spinning like a coin until flat again. This shape can be stretched in the middle, creating opposing whirlpools, or flattened out completely like the tornado we spin against. The top flattens until the whole tornado is on one plane. Hopf vibration explains magnetism very well.

[Yamikaiba]

Math is the study of symmetries; it is a logic of analogy at its very foundation.
Any reasoning that can be adapted by analogy will have generalizability. But what if that reasoning is the logic of analogy itself?
There is no such thing as 1, but if I say that a pencil is analogous to an orange in that there is 1 pencil and 1 orange, I have invented a concept that is useful for measuring pencils among pencils and oranges among oranges.
Math is so generalizable by its very nature as a logic of analogy.
-repeating this with a tip, because your answer to Why is Math So Useful prodded me to crystalize my feeling about it into words for the first time

[FunkyDexter]

S3 is important because it can be parallelized, unlike S2 (the normal sphere). Basically, you can't comb a hairy sphere without leaving a cowlick somewhere, but you can on the hypersphere. What's more, a parallelized 3-sphere looks like a normal 3D space, even though topologically it is four-dimensional. There is a relatively unknown version of GR called teleparallel gravity, the mathematics are equivalent but instead of assigning the cause of gravity to curvature, it is assigned to a torsion. One of the exact solutions to the Einstein equations is modeled by S3, which corresponds to a closed, curved universe.
As for the hopf fibration, which is fundamentally a projection of the higher dimensional topology, it models particle spin really well.

[tedsheridan]

The simplest way to understand a Hopf fibration physically is to consider a particle oscillating in two dimensions (double harmonic oscillator). Basically it's a mass/spring type system that moves in the x and y directions separately. There are four state variables - the x and y positions, and the x and y velocities (call them v and w). To plot them in state space you need four dimensions. Now constrain the total mechanical energy of the system to a constant value, and choose your constants and scaling factors so that this energy is 1. The total energy (kinetic and potential of both directions) is the sum of the squares of all 4 state variables, so x^2+y^2+v^2+w^2 = 1. This is the equation of a unit sphere in 4D (the 3-sphere). As the particle oscillates, the path in state space is a circle of radius 1, which lies on the 3-sphere. There are two ways you can alter this path. First you can change the phase difference of the oscillations, i.e. the amount that the y-oscillation leads or lags the x-oscillation. Each unique phase difference will have it's own circular path, and all of these paths together form a donut shape, where the donut of circular paths lies on the 3-sphere. Second, you can change the energy distribution - how much of the total energy is associated with the x-motion vs the y-motion. A large amplitude in x means a smaller amplitude in y. Every unique energy distribution has its own "donut" of paths. At the extremes the energy is all in the x or all in the y (a circular path for each), and in between you get donuts where each circular path corresponds to a specific phase difference.  
The reason it comes up so often is that it arises from simple math. You can model it with two complex numbers rotating around the origin at constant rate. If you constrain them so that so the squares of their magnitudes add up to 1 ( just like the energy constraint), you have the same two levers of control - the phase difference and the magnitudes of the complex numbers. Geometrically, the two control parameters (phase and energy), can be plotted on a regular unit 2-sphere - hence the mapping from S3 to S2. Each point on S2 corresponds to a unique circular path on S3. This exact situation comes up in a two state spinor system, and quaternion rotation, and it's not too hard to imagine that the same kind of math comes up in many different areas. 
Does that make it important? I mean linear equations, show up everywhere in physics. You might as well say that straight lines are the most important object in the universe.

[plainjane]

I agree with Curt, the effectiveness of mathematics is not unreasonable! It is in fact a direct outgrowth of our ability to apply reason to our actions and our theories.

Also: it seemed to me when listening to the two of you talk about the n-dimensional spheres, that Curt was thinking algebraically and Carlos was thinking more geometrically. But my math education is limited.

Off to see the whole episode.

[obsideonyx]

Can't believe two of my favourite people are talking.

[DevinDTV]

It is interesting how brilliant mathematicians and physicists can have such a poor intuition for philosophy. Curt's argument about math's effectiveness should be obvious yet somehow very few people can reach that conclusion on their own.

These people just have no idea how axiomatic systems work, despite making whole careers out of using them.

[consistent]

According to Wolfram, while the vast majority of the Ruliad is computationally irreducible, it contains an endless number of computationally reducible islands.
In these islands, where complexity may be tamed, we enjoy “the unreasonable effectiveness of mathematics” a la Eugene Wigner.
The unreasonable effectiveness we developed at leveraging this reducibility seduced us into neglecting our connection with the spirit, with the irreducible. It has left us stranded in an isolated realm of reductions - in our own self-referential prison of concepts and words that pose as reality. It is hard for us even to conceive that we may experience knowledge not through the veil of words.
Our triumph, however, will comprise of restoring our ability to grok, on occasion, reality as is (never fully, but as-is), unreduced and unmitigated by concepts and words, while maintaining our ability to leverage, on occasion, the knowledge and wisdom we gained while traversing the lands of Reason.
Bon Voyage! :)

[tuyg]

I believe the significance of Eric’s Geometric Unity is tied to the idea of using Geometry as a model to describe how information is able to be encoded within, as well as transferred across dimensions, with the S3 being contained within S2 feature of this theory, along with other permutations of a similar dynamic occurring with any type of S in particular, to essentially function as a way to take computation and translate that into physical form, and vice versa, which was indeed rather timely to the bring concept up, based on how that exactly notion was mentioned in a different clip from the same discussion.

[MikeThaPhilosopher]

When is that Lue video coming out? & how can I submit questions

[jr]

cool answers to the unreasonable effectiveness of math.

[Tripple_Threatt]

Please do a interview with Eric🙏🏾I feel your the only one with the mathematical & geometric knowledge who can also break things down into simple terms that can really explain this idea to a mass audience(me)😀

[russellturner]

It's because the basic ratios that math expresses *are* the local optima for our dynamic systems (or scalars therefrom)

[Yamikaiba]

Finally, you answered that Why is Math Effective question along the lines that satisfy my skepticism of the question.

[trevconn]

The fibers of the heart are VERY similar to the structure of the hopf fibration. Also similar to the mechanics of piezoelectrics, the hopf fibration can also allude to mechanics of gravity in Twister Theory and provide insight into torsion waves. A toroflux is a fun tool to visualize this.

[merlepatterson]

If one were to imagine a perfect sphere of any given diameter and then fill it with any number of imaginary filament lines from edge to edge within the sphere, it makes no difference what the filaments represent, a mathematically perfect sphere has only one edge (surface) thus the number of imagined filaments within it is redundant to the sphere residing within a mathematical area itself. The sphere fulfills its own representation.

[kevinsho]

Let's face it. Eric wants recognition and fame. He wants to be pictured as this unbelievable intellect. He likes to exaggerate situations and make attention-grabbing claims. I think he is a person who thinks he wants to answer big questions but doesn't realize he is looking more so to be an exalted person by the masses. If you watch him and his body language and listen to what he says, you can easily tell there is a high level of arrogance and self admiration. I think Eric is always trying to put on a show and act like he is some persecuted genius who has to do surreptitious work because academia is trying to hold down his world changing genius.

[Mattwatch]

I think what he was trying to say was that math is fundamental across the spectrum of studies in a unique way. Also, we invented knives and hammers, did we invent math? I think math is natural law or in other words reality itself, and we don’t think of reality as unreasonably effective, that would seem silly.

[atheios]

Curt, you are on to something here. It is directly analogous to evolution. We're here, because we can be here. We have the math we have, because it can be here. Doesn't that suggest a sort of proto-mathematics? A structure that all existing math stems from? Shower thoughts for days. Thanks for this video!

[paulthomas]

Who is the Carlos in this discussion? And what is his channel?