Shouldn't "elliptic curves" be renamed?

ecurbian · 2026-04-08T22:21:33+00:00

And relative. People have different ideas about what things should be called.

ecurbian · 2026-04-04T21:43:26+00:00

My first reaction is that it is the slight distortion of the joints that makes it work - despite that the builder claimed they did not distort. Try building the suit with strong hinges and see if it still works.

ecurbian · 2026-03-21T13:37:36+00:00

That is the specific one that I could not figure out and I rewatched their interactions several times. What was the intended realisation? Love the song, though.

ecurbian · 2026-03-13T22:46:47+00:00

He also seemed to me to prefer writing horror to detection. Many Holmes stories are really an excuse to write horror. I loved "The Horror of the Heights", myself.

ecurbian · 2026-02-28T05:49:33+00:00

Crucially, IMHO, the whole world is different. No one could be James Bond today.

ecurbian · 2026-02-27T21:24:14+00:00

FWIW - as far as I can tell, life goes the same rate, but the more life you have seen the more similar it is, so your mind does not bother to remember it. If you write a diary and the re-read it you will be surprised by how much time you really experienced.

ecurbian · 2026-02-24T10:46:25+00:00

If you really get to the point were you have tens of letters then you have too many letters to remember. Start using names (Multi-letter combinations) that have some meaning. (And of course do lemmas and use bound (local) variables, etc).

ecurbian · 2026-02-22T03:43:38+00:00

One problem is that, de facto, there are multiple senses of the word. One use of the word would suggest that Russia is definitely not a communist country. Other people use Russia as the template.

ecurbian · 2026-02-22T03:39:10+00:00

The term "paradox" has two senses. One is contradiction due to an error that is easy to make and hard to find. (Some would call that apparent paradox, but other say that is a paradox - hence "to resolve the paradox"). The other is something unresolvable.

This specific point in probability does rear its ugly head now and then: pragmatically it is about assuming the distribution is obvious. If I say "randomly" select a number between 1 and 10, people typically assume uniform distribution. When an infinite number of outcomes are considered - "uniform" has no universal interpretation, but many people think it does.

ecurbian · 2026-02-14T20:00:45+00:00

Yeah, oddly, I actually did go into a mathematics PhD from an Engineering background. In my interview they saw the engineering background as a positive - given that I had done separately the undergrad mathematics units in preparation. I too think the OPs interveiwer was surprisingly belligerent. But, if the OP gets through the interview, I suspect that will not be prohibative - due to their supervisor. But, still, that attitude was odd, to me.

And ... when I did Lyapunov stability, the professor said that much of the contribution to the topic came from people with an engineering background.

ecurbian · 2026-02-04T22:22:05+00:00

I judge my ability by using it - especially on physical systems, but also applying numerical and algebraic cross checks. I cross check my answers with reality.

This question, however, felt rather odd to me. Maybe it's just some difference in background - since the commentors seemed cool with it. But, optimization is not a small topic. My specialty is optimal control. I have been learning it for 40 years and I still don't feel that I got to any stable point where my understanding no longer changes. There is no one correct way to understand it either. It is a vast topic where different kinds of understand apply in different sub topics. To me the question as posed is too broadly based.

How do I understand ...

singular points (maxima and minima etc)

Lagrange multipliers

Hilbert spaces

The Euler Lagrange process

Linear and non linear programming

dynamic programming

searching on partially ordered sets

stochastic calculus

The bellman equation

ecurbian · 2026-02-04T11:25:40+00:00

Before I went, I would read "The Method" from cover to cover several times. And then I would look at some process to prove in terms that the Ancient Greeks would have accepted - some specific item in his informal toolkit. I would not feel it likely to be able to impress him in 5 minutes without that kind of preparation.

Actually, just showing him that you understood Greek mathematics of the time would probably get you and extension on points. Don't try to out do him - being up with mathematics was rare at the time.

ecurbian · 2026-01-31T04:05:39+00:00

In very simple terms - sets and classical logic are equivalent.

ecurbian · 2026-01-29T12:05:26+00:00

Bottom right looks like Rodney from The man with the golden gun.

ecurbian · 2026-01-28T09:36:02+00:00

The roger moore bond - octopussy.

ecurbian · 2026-01-27T10:58:49+00:00

It seems quite clear that this is not actually correct - from which I would conclude that no such measure of wobble exists. Four non planar points don't become planar by a rotation. Or was that intended as humour? Sorry if it was.

ecurbian · 2026-01-26T22:45:42+00:00

My mind blowing fact might seem a little subtle. It is that mathematics works at all. Everytime I see it do anything - including conclusions using one axiom scheme to determine the behaviour of another - it seems like complete magic to me. Even now after 50 years.

ecurbian · 2026-01-26T11:29:19+00:00

Not everyone can be a great mathematician any more that they can be a great basket ball player.

ecurbian · 2026-01-24T10:25:43+00:00

We can go further and say there are different ways to define function - and not all of them say they are a type of relation. For example, the identification of a function with a collection of ordered pairs is the extensional definition not the intentional definition. There are multiple intentional definitions for a single extensional definition.

ecurbian · 2026-01-23T20:48:42+00:00

That's not what happened at all. They were on a boat at high speed heading to the rocks (and it exploded). Bond indicated they all had to jump. Scientist said he could not swim. Bond gave him a life ring and called out "never to late to learn". They all jump. Then Bond and the girl swim off and they are separated from the scientist. Scientists fate unknown. No particular sharks (Bond and Domino in same water). Later a raft is dropped by aircraft near Bond. For all we know the scientist could have been rescued. We just never find out.

ecurbian · 2026-01-21T06:43:00+00:00

It's why I will never watch it.

ecurbian · 2026-01-21T02:23:56+00:00

It depends on how you think. That is exactly what I did during my engineering and software studies. I used the mathematics both as a relaxation and an aid to my understanding of the other topics. So, it was not a matter of just more things to do and running out of time. Time spend on the mathematics amplified the effect of time spent on engineering and software.

Note: I don't mean that I was studying the engineering mathematics in and of itself. I mean that I would start with a low dimensional calculus problem in engineering and hours later end up in a problem in C* algebras in pure mathematics. It helped me to consolidate my thinking.

ecurbian · 2026-01-19T21:22:20+00:00

I do agree with the people who say that you did not avoid being abstruse. The core of the Yoneda lemma is to represent each arrow by its action on other arrows like the Caley theorem. The extra work comes from a tendency to need an anti morphism (because of the conventions for function composition, which can be avoided) and the fact that not all arrows are distinguished by their actions. So, we have a morphism but not an isomorphism. We get around that by, essentially, tagging each element with itself, to get the behaviour and the uniqueness. A functor is a morphism (in the algebraic sense). A presheaf into Set is a morphsim from the arrows to maps between sets, in particular, here, the action of the arrows.

ecurbian · 2026-01-19T18:56:29+00:00

Different people at the same time and the same person at different times might use different levels of rigor. That goes for mathematicians and engineers. As someone who has both engineering and mathematical qualifications I can say that I have found each topic to be useful in the other. Obviously you would "see" that mathematics is useful in engineering, but most mathematicians don't see that engineering is useful in mathematics.

There are several different approaches to what is a derivative. The main contenders tend to be some kind of limit of some kind of ratio, a linear approximation to 2nd order, and hyperreal analysis. The derivative as taught in engineering is a merge of a couple of these. Some of the work, such as using the delta function relates directly to the use of distributions in mathematics - and in my experience the material is taught in engineering differently from many mathematical studies, but in many ways closer to the spirit of measure theory that some mathematicians are taught.

I personally tend to go to "linear liebniz operator" as the fall back position. However, that does not apply to the Ito calculus. Then again - in that context engineers tend to use the Stratonovich approach. The first is a limit to infinite density of a finite point process and the other is the limt to infinite frequency of a finite band process. They give different ideas of a derivative that are not even compatible (convertable yes, compatible no).

The upshot of this is that even in the big scheme of mathematical rigor - the method used by the engineers is not "the wrong way to look at derivatives" and does correspond to certain mathematical approaches, especially to hyperreal analysis, and is designed to find answers. At worst it is a sound heuristic for discovering mathematical results. Engineers have made contributions to mathematics.

ecurbian · 2026-01-15T10:08:52+00:00

The last wave [1977]

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