bitdizzy

I've been following this discussion closely because I work in adjacent areas and have dipped into Coq and Agda. Now that I see it on hackernews and all sorts of comments speculating on how this is cancel culture and English-centric chauvinism I'm really disappointed. Sometimes you lack the social context to evaluate the merits of a discussion so you default to your image of the most plausible motivation and it says a lot in this case. A popular idea here is the "gellman amnesia effect", yes? Well I'm definitely not going to forget this in the broader context every time a post comes around baiting culture war rhetoric.

Unfortunately some women actually in the Coq community discussing this on Twitter noticed they were getting all of a sudden a lot more engagement with concern trolls around the time this submission gained traction. "intellectual curiosity" indeed. I hope its worth it, this place existing. I think I can find a replacement though so I'm logging off indefinitely.

Almost by definition society is the negotiation of our behavior toward each other because otherwise we would impinge on each others' freedom to act as we please in intolerable ways.

Perhaps you think that is a bad thing and to be honest i wouldn't blame you if you decided to ignore all laws and norms of society and behaved like a feral animal towards others. I just don't think you would get very far before you're put in a cage or gunned down.

What people say are their values and the values revealed by their actions can be different. Moreover one can express certain values in pursuit of goals that are incompatible with those values. This is styled hypocrisy and the bourgeoisie such as Thiel are very used to this.

We live in a society

> I am curious as to how?

Special relativity describes a flat lorentzian manifold. The uniform expansion of the universe implies that the curvature of spacetime is slightly negative.

Special relativity is not simply a theory of causality but specifically of the geometry of spacetime. From this theory you can derive predictions about specific phenomena, like causality.

But that doesn't mean other spacetime geometries don't share properties with flat minkowski spacetime. Just not all properties. For example there is no cosmological horizon in minkowksi spacetime but there is for our universe.

Non-measurable sets are precisely the kinds of things Arnold wanted marginalized in mathematical pedagogy, instead of placed front and center. They are necessary auxiliaries to the main theory, that of measures and integration but auxiliary nonetheless.

I disagree that transfinite numbers are detached from physical intuition since most of the ones you or I could write down can be easily visualized with a few ellipses here or there. But i do think Arnold would consider them marginal players. Perhaps he thought set theory was a formalist distraction from the main of mathematics!

The first use of complex numbers was as intermediate quantities in the calculation of the roots of cubic polynomial functions. This use is analogous to using negative numbers in a ledger even though negative amounts of physical things don't make sense.

Edit: I meant physical things like apples fam. This is an important philosophical point we don't appreciate because we are so used to them. De Morgan once wrote:

"It is not our intention to follow the earlier algebraists through their different uses of negative numbers. These creations of algebra retained their existence, in the face of the obvious deficiency of rational explanation which characterized every attempt at their theory."

For Arnold, mathematics is rooted in physical intuition and experimental inquiry. Can you name some math that is completely disconnected from that intuition?

A lorentz boost is just a change of perspective. Let's say you have a bubble that is at rest with respect to your reference frame. Well, someone flying by your solar system has just as valid a reference frame as you and they see the bubble moving with respect to them. The relation between their point of view and yours is described by a lorentz boost. Same physical situation, different perspective.

Now, if special relativity holds in the large then there is no reason why they can't also construct a warp bubble. Relative to you and your bubble that bubble is in motion. Since this is allowed, we can construct a closed timelike curve with two judiciously chosen bubbles.

> Which the universe kinda already does, no?

The expansion of the universe does violate special relativity but not in a way that protects warp geometry from creating paradoxes. The kind of violation you would need would distinguish between frames of reference that SR says are equivalent.

> And further, doesn't special relativity already only hold in cases with low gravitational potential - so i.e. not in a gravitational field?

Special relativity holds well enough in most situations that the same argument applies even if you accounted for general relativity except near extreme situations like black holes

Warp drives are not permitted by any deviation from special relativity. You need specific contrived geometries of the entire universe that don't match up with what we know about it.

Why is this obviously wrong?

So the thing that paper does is it assumes you can make warp bubbles in any reference frame. The original paper makes one warp bubble and this doesn't lead to anything paradoxical.

But if I can make two warp bubbles in two different frames, I can make a round trip that arrives before it starts.

So you need to violate special relativity in a global way to avoid these issues. You have to have a spacetime where only certain warp geometries are possible.

I apologize for being a bit impatient before, these issues are subtle. The only real way to get it is to bear with the math onesself.

it's not like a thunder storm. The wikipedia page has a worked out example. If you can go back and forth between 2 places FTL you can arrive before you left and interfere with your departure.

You are more convinced by a metaphor than the actual theory of relativity. That can't be helped.

Volunteering yourself, or others?