Very interesting article.
This makes me wonder: Would it be possible to implement an equivalent to Shor's algorithm on a p-computer. Maybe the quantumness isn't necessary at all
Readit Newsm_dupont commented on Elon Musk and the right's war on Wikipedia citationneeded.news/elon-... · Posted by u/throw0101d
I think there is some room for debate here about the political bias of wikipedia, and there is some evidence to suggest a left wing bias.
However this article is pretty venomous and the author doesn't even make an attempt at masking their disdain for the other side. It's not written in good faith.
I'd prefer if someone shared a more cool-headed article on the subject
m_dupont commented on How has mathematics gotten so abstract? lcamtuf.substack.com/p/ho... · Posted by u/thadt
>Next, consider the time needed for Achilles to reach the yellow dot; once again, by the time he gets there, the turtle will have moved forward a tiny bit. This process can be continued indefinitely; the gap keeps getting smaller but never goes to zero, so we must conclude that Achilles can’t possibly win the race.
Am i daft, eventually (Very soon) Achilles would over take the turtles position regardless of how far it moved... I am missing something?
you're not, the proof is a famous error known as zenos paradox. Its only an apparent paradox, and indeed it's been disproven by observing that things do in fact move
m_dupont commented on A fast, strong, topologically meaningful and fun knot invariant arxiv.org/abs/2509.18456... · Posted by u/bikenaga
They mean that their invariant does a good job of distinguishing different knots from one another.
The way they quantify this is: they pick a biggish set of knots that are known all to be distinct from one another. They then compute their invariant for each of those knots. A knot invariant successfully distinguishes them all from one another precisely when it takes different values for all of the knots. So they count the number of different values their invariant takes, and subtract it from the number of knots. They call this the "separation deficit": the smaller the better.
They compare their invariant with some already-known ones, taking "all knots that can be drawn in the plane with <= 15 crossing points" as their set of knots. There are about 300,000 of these.
One of the best-known knot invariants is the so-called Alexander polynomial. That's in row 3 of Table 5.1, and its "separation deficit" for those knots is on the order of 200k. That is, these 300k knots have between them only about 100k different Alexander polynomials; if you pick a random smallish knot and compute its Alexander polynomial then handwavily you should expect that there are two other different smallish knots with the same Alexander polynomial.
Another knot polynomial, which does a better job of distinguishing different knots, is the so-called HOMFLY polynomial. (Why the weird name? It comes from the initials of the six authors of the paper announcing its discovery.) That's row 7, showing a deficit of about 75k. That suggests, even more handwavily, that if you pick a random smallish knot and compute its HOMFLY polynomial, there's about a 1/3 chance that there's another smallish knot with the same HOMFLY polynomial. Still not great.
A rather different sort of invariant is the hyperbolic volume of the complement of the knot. That is: if you take all of space minus the knot then there's a certain nice way to define distances and volumes and things in the left-over space; the whole of space-minus-the-knot turns out then to have a finite volume, and perhaps surprisingly deforming the knot doesn't change that volume. So that's another knot invariant, and it turns out to be better at distinguishing knots from one another than the polynomials mentioned above, on the order as 2x better than the HOMFLY polynomial.
This paper's invariant (which is a pair of polynomials) does about 6x better than what you get by looking at the Alexander polynomial, the HOMFLY polynomial, the hyperbolic volume, and a few other invariants I didn't mention above, all together. Its "separation deficit" on this set of ~300k knots is about 7000. If you pick a random smallish knot, there's only about a 2% chance that some other knot has the same value of this paper's invariant.
(Reminder that all this business about probabilities is super-handwavy. Actually, that probability might be anywhere from about 2% to about 4% depending on exactly how the values of the invariant are distributed.)
Now, all of this is purely empirical and looks only at smallish knots. So far as I know they haven't proved any theorems like "our invariants do a better job than the hyperbolic volume for knots with <= N crossings, for all N". I think such theorems are very hard to come by.
They don't, to be clear, claim that their invariant is the best at distinguishing different knots from one another. For instance, they mention another set of knot polynomials that does a better job but is (so they say) much more troublesome to compute for a given knot.
very clear and detailed answer. thankyou very much
m_dupont commented on A fast, strong, topologically meaningful and fun knot invariant arxiv.org/abs/2509.18456... · Posted by u/bikenaga
To their credit, the paper is unexpectedly fun.
I'm not understanding the "separation power" thing, what does that imply?
If chat control gets passed it will also be a law, passed by legislation.
The point is that laws can be unjust.
m_dupont commented on · Posted by u/NomDePlum
May or may not be true but it's completely unrelated to tech, science or startups.
This should be moderated
Small piece of product feeback related to grammar:
The landing page asks, how are you feeling? For which the possible responses are "Anxiety", "Procrastination" ... "Overwhelm".
When a person says, I a X, X is always an adjective. One doesn't say "I am Irritability" one says "I am irritable".
All of these options are nouns, except for "Overwhelm" which is actually only a verb but is being used incorrectly as a noun.
The correct responses would be "Anxious", "Hyperactive", "Overwhelmed", "Irritable".
Except for "Procrastination", which doesn't have any associated adjective. You might need to rephrase the whole header
My Qualifications: I moved to Germany for 7 years
I can only add my voice to what others have said: Just apply to universities and get your student visa.
In general it is very difficult applying to jobs in countries from abroad, and in many countries they have laws requiring that companies must prove that they couldn't source talent locally first.
Meanwhile student visas are very easy to get, and after you are in the country on a student visa, you can seek part time work, or get a job as soon as you graduate. Many countries offer fast-track residence permits for expats who have graduated from one of their universities.
My story: I applied to a german university, got accepted, and got the student visa relatively painlessly. After graduating I found a job relatively quickly and got a work permit.
I have some more tips, specifically pertaining to Germany and your requirements:
> Language: In Germany you can get around no problem with 0 German. Me personally I downloaded Duolinguo the day before my flight and I did just fine learning as I went.
> EU financial foundation: I'd say you can just build a US financial foundation then send it over via bank transfer when u arrive.
> Established living situation: If you get accepted to a german university, try to show up at least a month before courses start. Take that time to open a bank account, get insurance, enrol and find an apartment. Do NOT try to find a rental when you don't have boots on the ground, there are a bunch of scams that target international students trying to secure accomodation. For your first month or so, just stay in an airbnb until you find a place you like long-term
>
One of the most fundamental reasons for my own personal loneliness is that, in many of the connections I've made, they simply do not feel sincere, genuine, authentic, and simply because the other person clearly has a different motivation for "caring" about me than actually caring about me.
For example, the churchgoers I've met have always felt like they were only spending time with me to get me to become a member of their church. They were eager to throw money at me if I lost my job, or offer to help me move, but never wanted to get coffee outside church hours.
Therapists are another example, obviously financially incentivized to talk to me. There are definitely some who care simply because it's part of their personality, but that still says nothing about me and any connection they have with me.
And I shared a story elsewhere here of a priest who I had literally just met minutes before, and who actually went in for a hug the moment I mentioned having a hard time with something, as if this random hug from a complete stranger meant anything other than him following a virtue signalling script.
No, I am convinced that the solution must be free, it must be volunteers doing it without anyone knowing about it, without the belief that they're earning brownie points from God or gaining a potential member of some organization, and without getting paid or rewarded for it, except for the reward of having a new and worthwhile friendship with the lonely person.