@internic@qoto.org
@internic@qoto.org avatar

internic

@internic@qoto.org

Theoretical physicist by training (PhD in quantum open systems/quantum information), University lecturer for a bit, and currently paying the bills as an engineer working in optical communication (implementation) and quantum communication (concepts), though still pursuing a little science on the side. I'm interested in physics and math, of course, but I enjoy learning about really any area of science, philosophy, and many other academic areas as well. My biggest other interest is hiking and generally being out in nature.

This profile is from a federated server and may be incomplete. Browse more on the original instance.

grimalkina, to random
@grimalkina@mastodon.social avatar

I'm sorry WHAT and none of you told me?????

Position ENTIRELY reversed on Python. Literally going to learn it now. Call me pythonista Cat. I am so serious. WHAT.

https://masto.machlis.com/@smach/112462436451472935

internic,
@internic@qoto.org avatar

@grimalkina Historically not a Python fan?

johncarlosbaez, (edited ) to random
@johncarlosbaez@mathstodon.xyz avatar

There's a dot product and cross product of vectors in 3 dimensions. But there's also a dot product and cross product in 7 dimensions obeying a lot of the same identities! There's nothing really like this in other dimensions.

We can get the dot and cross product in 3 dimensions by taking the imaginary quaternions and defining

v⋅w= -½(vw + wv), v×w = ½(vw - wv)

We can get the dot and cross product in 7 dimensions using the same formulas, but starting with the imaginary octonions.

The following stuff is pretty well-known: the group of linear transformations of ℝ³ preserving the dot and cross product is called the 3d rotation group, SO(3). We say SO(3) has an 'irreducible representation' on ℝ³ because there's no linear subspace of ℝ³ that's mapped to itself by every transformation in SO(3).

Much to my surprise, it seems that SO(3) also has an irreducible representation on ℝ⁷ where every transformation preserves the dot product and cross product in 7 dimensions!

It's not news that SO(3) has an irreducible representation on ℝ⁷. In physics we call ℝ³ the spin-1 representation of SO(3), or at least a real form thereof, while ℝ⁷ is called the spin-3 representation. It's also not news that the spin-3 representation of SO(3) on ℝ⁷ preserves the dot product. But I didn't know it also preserves the cross product on ℝ⁷, which is a much more exotic thing!

In fact I still don't know it for sure. But @pschwahn asked me a question that led me to guess it's true:

https://mathstodon.xyz/@pschwahn/112435119959135052

and I think I almost see a proof, which I outlined after a long conversation on other things.

The octonions keep surprising me.

https://en.wikipedia.org/wiki/Seven-dimensional_cross_product

internic,
@internic@qoto.org avatar

@johncarlosbaez A very basic question: What does "the cross product on R^7" mean? I'm familiar with defining an antisymmetric product in n dimensions in the form of the exterior product, but I'm only familiar with how to map the result to an individual vector in 3 dimensions (via the Hodge duality). @pschwahn

internic,
@internic@qoto.org avatar

@johncarlosbaez What I meant was that, while for other operations like the dot product the definition is independent of dimension, the only definition I know for a cross product is specific to 3 dimensions, so I wasn't really sure what the claim "it's the 7-dimensional cross product" is supposed to imply, exactly.

Based on your mention of it "obeying the usual identities," I'm guessing on an arbitrary vector space it's defined to be a mapping V^2 -> V that's bilinear, antisymmetric, associative, and then obeys the same identities with the dot product as in R^3.

internic,
@internic@qoto.org avatar

@ppscrv @johncarlosbaez One might argue that spelling things out in painful detail is basically the definition of pure mathematics. ;-P

internic, to mastodon
@internic@qoto.org avatar

Just noticing that it looks like the @arstechnica account stopped posting here about a month ago. #Mastodon

internic,
@internic@qoto.org avatar

@peterdrake @MichaelPorter Ah, okay, thanks for the sleuthing. I was aware of some other things being broken but not this sort of phenomenon. Glad to hear @arstechnica is still posting on mastodon. @freemo

internic,
@internic@qoto.org avatar

@freemo Thanks for the update! @peterdrake @MichaelPorter

elizabethtasker, (edited ) to random
@elizabethtasker@mastodon.online avatar

OK, OK... so IMPORTANT QUESTION. Can we say "globally" when discussing the entire surface of a celestial body such as Phobos? That Martian moon baby isn't remotely spherical. It's a potato.

internic,
@internic@qoto.org avatar

@elizabethtasker The heliosphere and the magnetosphere aren't spherical, and they have sphere in the name, so it seems like you should be able to get away with "globally" here. :-)

idoubtit, to random
@idoubtit@mstdn.social avatar

🙄 No one learns anything anymore. 😒

https://www.engadget.com/bluesky-now-allows-heads-of-state-to-join-the-platform-202700504.html

internic,
@internic@qoto.org avatar

@idoubtit I'm curious, what alternative policy would you advocate?

elizabethtasker, to random
@elizabethtasker@mastodon.online avatar

Went to a little takoyaki stall that advertised as new and in truth… had a single worker who I’m not sure had ever made takoyaki before! It tasted fine, but took a loooooong time to prepare (it’s usually a fast food from a stall that is more experienced) 😅🐙

The takoyaki: 7 battered balls with mayonnaise on the top.

internic,
@internic@qoto.org avatar

@elizabethtasker No bonito?

grimalkina, to random
@grimalkina@mastodon.social avatar

I swear I'm going to do a research study someday that's called "Do All Engineers Magically Turn Evil Once Promoted Into Leadership: Seems Unlikely"

internic,
@internic@qoto.org avatar

@grimalkina It has always seemed to me that the skills required for leadership/management are significantly different than many of the skills required to excel technically as an engineer. Yet it also seems like engineers are frequently "promoted" to management/leadership because of technical success, so you essentially have people being given a job based on the wrong qualifications. It's hardly a novel insight, I'm sure, but I'm curious for your much more educated perspective.

strypey, to random
@strypey@mastodon.nzoss.nz avatar

Can anyone recommend a Free Code platform for collaborative authoring?

I'd like to be able to write a book in a sort of wiki - with a wiki page for each book page - which trusted contributors can edit. Plus an ability for anyone to comment on each page, using an account on the platform.

Bonus points if the WIP is federated over ActivityPub, and people can use their fediverse accounts to comment. Allowing a broad range of contributions while using fediverse moderation tools to reduce noise.

internic,
@internic@qoto.org avatar

@strypey @liamdiprose @hobs Right. I've used source control products to collaboratively write documents in LaTeX, so I'm philosophically sympathetic to the suggestions being made here, but I don't think they're really appropriate for the use case described in the OP.

  1. LaTeX is great, but it has a steep learning curve and is not widely known outside of certain STEM fields (and even then it seems to mostly be used among researchers).
  2. Source control tools are probably the most powerful solution for collaboratively editing documents, but they also have a steep learning curve and are not really known by non-programmers. I've even had issues getting STEM folks to really wrap their heads around it.
  3. While you can use an issue tracker or similar mechanisms to track meta-discussions among authors, this is, again, not the natural way people are used to doing this if they are not programmers.

It sounds like the intended use case is to have collaboration with a wide range of authors, which seems to make the foregoing deal killers (unless they're all scientists who write code or something).

I'm guessing some of the suggestions like asciidoc or pandoc are a bit more on target, but a solution that presents more user interface for contributions and comments seems more ideal. I don't have a strong suggestion, but I did think about Wikibooks as one possibility (but not necessarily the best one). I think that just uses MediaWiki but maybe with some specific customizations.

internic,
@internic@qoto.org avatar

@strypey @liamdiprose @hobs Yes, that's the Wikibooks I was referring to. I think right tool depends on your intended community of authors. If they were all, say, mathematicians or computer scientists, then LaTeX + Git could be a great solution. If you instead want people to collaboratively right about history, then it would probably be a terrible solution, because they would find it too opaque. What is your intended community of collaborators?

As for git, given that even many programmers complain about how opaque and complex it can be, it's not a tool that I would spring on anyone without a programming or math background, personally.

internic,
@internic@qoto.org avatar

@strypey @liamdiprose @hobs I believe that could be done in principle, but I have yet to see one in reality.

johncarlosbaez, (edited ) to random
@johncarlosbaez@mathstodon.xyz avatar

Hardcore math tweet:

The complex numbers are nice in two ways. They are an 'algebraically closed' field, meaning that every polynomial equation with complex coefficients has a complex solution. And they are 'Cauchy complete' metric space, meaning that every Cauchy sequence converges.

We can get the complex numbers in two ways. We can start with the rational numbers and take their Cauchy completion. This gives us the real numbers. But these are not algebraically closed. So we can take their algebraic closure. The result is the complex numbers, which is still Cauchy complete.

Or, we can start with the rational numbers and take their algebraic closure. This gives us the 'algebraic numbers'. There's a way to define a nice metric on these, but the resulting metric space is not Cauchy complete. To fix that, we can take its Cauchy completion. The result is the complex numbers, which is still algebraically closed.

In the first route I used the usual metric on rational numbers. But what if we use one of the p-adic metrics?

We can start with the rational numbers and take their Cauchy completion using the p-adic metric. This gives us the p-adic numbers. But these are not algebraically closed. So then we can take their algebraic closure. There's a nice metric on it, but it's 𝑛𝑜𝑡 still Cauchy complete.

So we can take the Cauchy completion 𝑎𝑔𝑎𝑖𝑛. You may feel sort of pessimistic right around now... but this time the resulting field 𝑖𝑠 algebraically closed, and of course Cauchy complete by definition. So yay, we're done! 🎉

The weird part: the resulting field is isomorphic to the complex numbers equipped with a weird metric. Using the axiom of choice. 😬

internic,
@internic@qoto.org avatar

@johncarlosbaez That's fascinating! Unfortunately I've only had limited exposure to the p-adic numbers, so I can't entirely appreciate this, but you've definitely piqued my interest.

internic, to math
@internic@qoto.org avatar

A question for real mathematicians out there (or at least the math rigor curious): Do folks in maintain consistent distinctions between the meaning of the terms "outer product" and "tensor product" (and for bonus points throw in "Kronecker product")?

I learned these concepts mostly from physicists (which is a bit like learning manners from being raised by wolves), and there was a tendency not to use consistent terminology or draw clear distinctions, though sometimes they were being used to refer to slightly different, but related, things. I could generally follow the sense in which terms were being used in a given application by context, so I didn't worry about it too much. A cursory look online also suggests that usage is heterogeneous, but I'm curious if mathematicians are, in fact, a bit more consistent.

mcnees, to random
@mcnees@mastodon.social avatar

Elf -> Elves
Dwarf -> Dwarves
Smurf -> Smurves

internic,
@internic@qoto.org avatar

@mcnees Proof -> Prooves?

internic, to random
@internic@qoto.org avatar

One more reason not to use X (a.k.a. Twitter): links may actually be taking you to a malicious site rather than where the preview claims.
https://lifehacker.com/tech/its-not-safe-to-click-links-on-x

johncarlosbaez, (edited ) to random
@johncarlosbaez@mathstodon.xyz avatar

I dreamt that an evil magician had cast a spell on my country. For those who had fallen under his spell, anything he said became true. Most of us knew better - we could see right through him. But it was hard to mount an effective resistance, since those under his spell included many judges, governors and senators. Others, well aware of his trickery, simply gave up resisting it - or shrugged it off as unimportant. Still more played along for their own venal reasons. Then one of my friends fell under the magician's spell. I tried to reason with them, I pleaded, I begged them to shake off the enchantment - to no avail. With an increasing sense of horror, I eventually woke up, twitching in my bed.

internic,
@internic@qoto.org avatar

@sliverdaemon But as @johncarlosbaez is alluding to there are also just many instances of not agreeing on the facts (e.g. related to the 2020 election). Differences in values have always been a central part of politics. It is disagreeing on observable facts that is disorienting.

grimalkina, to random
@grimalkina@mastodon.social avatar

Fascinating that the current extremist political rage tactic trying to destroy the careers of academics is "plagiarism" detection at the same time as all this AI hype stuff. Sometimes I'm like damn maybe Jung was right about it all

internic,
@internic@qoto.org avatar

@grimalkina It is a rather odd dichotomy, now that you mention it. On the other hand, I guess the people making the plagiarism accusations are unconcerned with either truth or intellectual consistency.

wtwagg, to random
@wtwagg@mastodon.social avatar

deleted_by_author

    •
    internic,
    @internic@qoto.org avatar

    @wtwagg Here's a reply. Hope your new setting works.

    dgoldsmith, to random
    @dgoldsmith@mastodon.social avatar

    Still waiting for someone on Threads I want to follow who isn't already on the Fediverse too…

    internic,
    @internic@qoto.org avatar

    @dgoldsmith My impression was that there were only a very limited number of people on Threads that it's possible to follow for Mastodon. Has that changed? I couldn't immediately find any way to discover who could be followed from here.

    duetosymmetry, to random
    @duetosymmetry@mastodon.social avatar

    Word cloud generated from your Google Scholar profile! What's yours look like? https://shiny.rcg.sfu.ca/u/rdmorin/scholar_googler3/

    internic,
    @internic@qoto.org avatar

    @johncarlosbaez Wait, how can categories be so small there? @duetosymmetry

    grimalkina, to random
    @grimalkina@mastodon.social avatar

    Ugh I miss being online with social scientists and getting to have a community of practice. God there is no place for it anymore.

    internic,
    @internic@qoto.org avatar

    @grimalkina I've seen physics and math academics bemoaning the same thing here. I hadn't really been participating in Twitter for professional purposes, so I haven't had the same experience personally. I was hopeful for some good physics conversations, but while there are some interesting folks here, overall it seems pretty quiet and conversations just seem to fizzle out pretty quickly.

    Ericlaw, to random
    @Ericlaw@mastodon.social avatar

    Tip: Microsoft Defender for Endpoint's Web Content Filtering has an option to block traffic to newly-registered domains.

    Vaporize a category of spear-phishers in their tracks.

    internic,
    @internic@qoto.org avatar

    @Ericlaw I believe you can get some similar functionality with NextDNS based on discussion by @henry on @techlore. Obviously that doesn't block all traffic, just DNS resolution, but that's probably enough in many cases.

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