@RobJLow@mathstodon.xyz
@RobJLow@mathstodon.xyz avatar

RobJLow

@RobJLow@mathstodon.xyz

Was a maths lecturer, main research interest general relativity. Now retired, rebooting as a classics undergrad at Warwick University. Still https://mathstodon.xyz/@RobJLow on Twitter: seeing how that goes.

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

monsoon0, to random
@monsoon0@mathstodon.xyz avatar

A proof is an amazing wonderful 🎉 thing… So I am wondering why the word “only” is in this sentence: “Researchers have obtained only mathematical proofs that quantum computers will offer large gains over current, classical computers” https://www.nature.com/articles/d41586-023-01692-9

RobJLow,
@RobJLow@mathstodon.xyz avatar

@johncarlosbaez @monsoon0 @drdunk I have nothing substantial to add, just the observation (probably unnecessary for most people on mathstodon, but just in case it helps) that the reason log N matters is that it is (roughly) the number of digits in N, so it's the size of the input representing N, and complexity is usually measured in terms of the size of the input.

ColinTheMathmo, to random
@ColinTheMathmo@mathstodon.xyz avatar

I can see a problem here.

(Found by @ghira ...)

RobJLow,
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@ColinTheMathmo @ghira Apparently they send out different form for people born before and in/after 2000.

henryseg, to random
@henryseg@mathstodon.xyz avatar

Apologies in advance to the mathematicians who follow this link: https://cims.nyu.edu/~tjl8195/survey/results.html

RobJLow,
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@henryseg Well, that's several minutes I'm not getting back. But for once, I don't resent it - time well and entertainingly spent :-)

ColinTheMathmo, to random
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Contractions function almost identically to the full two-word phrase. But they are only appropriate in some places in a sentence. It's one of the weird quirks of this language we've.

RobJLow,
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@ColinTheMathmo Never thought about it before, but do we only (I'm sure it's mostly) contract have to 've when it's an auxiliary verb rather than a main verb? I can't think of a natural sounding contraction when it's a main verb but it's one of those things that's hard to do when you're paying attention...

j_bertolotti, to random
@j_bertolotti@mathstodon.xyz avatar

The reason we use Calculus for just about everything in science is that it is MUCH simpler than the alternative.
(If you are unconvinced, try solving a Diophantine equation and come back to me.)

RobJLow,
@RobJLow@mathstodon.xyz avatar

@j_bertolotti Kind of ironic that we often start of with a discrete model of some kind, go to the continuum limit, get a differential equation out of that, then solve the differential equation numerically by approximating it as a difference equation.

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

This must be a solved problem ...

A group I'm in is reviewing and revising a document. It's a word document, because some of them are seriously, seriously technically challenged, and that seems to be the only thing they can cope with.

But making comments on and passing copies around of a Word document is just a completely nightmare, and it ends up ... as you will all know ... a mess of formatting, wrong versions, just ... urgh.

If there is a website with the document visible and little boxes spread throughout into which people can type comments to be collected and collated, that would be much easier.

Is there such a thing?

RobJLow,
@RobJLow@mathstodon.xyz avatar

@johncarlosbaez @davidsuculum @dougmerritt it won't be long before it's annoyingly difficult not to use it, I fear.

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

WHAT MAKES PLANTS GO BAD?

Why do plants become carnivorous?

They do so only when it's very hard to get nutrients like nitrogen. They still get their energy from photosynthesis, and it costs a lot of energy for them to be carnivorous. So they only arise in unusual environments like acidic bogs that are nitrogen-poor but sunny. And some cease to be carnivorous in the winter, when there's less light.

There's a continuum of plants ranging from noncarnivorous to so-called "protocarnivorous" plants to fully carnivorous plants. Protocarnivorous plants trap and kill insects or other animals but don't have special enzymes to digest their prey. Some of these evolve to become carnivorous. But don't think of evolution as goal-directed: depending on changes in their environment, some evolve away from being carnivorous. It's mainly a matter of how easy it is to get nitrogen.

There's an interesting conflict in this game. Plants have many clever ways of trapping insects and forcing the insects to pollinate them. This is a perfect first step in becoming protocarnivorous. But this sets up a battle of competing forces: will evolution optimize the trap for pollination or for killing insects and feeding the plant?

This is called the 'pollinator-prey conflict'. Many carnivorous plants try to have it both ways! And some are good at releasing insects that pollinate the plant, while killing others.

The game gets more complicated, too. One species of tree frog in Borneo specializes in eating insects caught in pitcher plants. And there's an ant that dives into pitcher plants to eat insects caught there - and also lubricates the top of the plant to make it easier for insects to fall in!

RobJLow, (edited )
@RobJLow@mathstodon.xyz avatar

@johncarlosbaez I'm getting quite a strong 'feed me, Seymour, feed me' from that image.
https://youtu.be/KNHrzZUascE?si=PaCDKAk0BRX_W0jY

ColinTheMathmo, to random
@ColinTheMathmo@mathstodon.xyz avatar

Your shadow shows that light has come nearly 150 x 10^9 m, only to be deprived of reaching the ground in its final metre, thanks to you.

RobJLow,
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@ColinTheMathmo I refuse to feel guilty, on the grounds that the mean free path of a photon in the air is less than a micrometre. (I also refuse to consider the relationship between photons and 'light', because that makes my brain hurt.)

mcnees, to random
@mcnees@mastodon.social avatar

Stephen Hawking's "A Brief History of Time" was published in 1988.

I read it a few months later, excitedly underlining and starring passages that wowed me, and spent the summer daydreaming about big bangs and black holes.

https://www.hawking.org.uk/in-print/books/a-brief-history-of-time?position=13

RobJLow,
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@johncarlosbaez it's also more intelligible than "brief history" 😬

ColinTheMathmo, to random
@ColinTheMathmo@mathstodon.xyz avatar

Which letter in 'Scent' is silent? The 'S'? Or the 'C'?

RobJLow,
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@ColinTheMathmo Is there such a thing as a rhetorical question?

ColinTheMathmo, to random
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Today's maths PSA: Events of probability 0 are not necessarily impossible.

RobJLow,
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@ColinTheMathmo I've always been fond of the paradoxical seeming fact (for some value of 'fact', v.i.) that if you choose a real number at random between 0 and 1, then with certainty (which is stronger than 'with probability 1'), an event of probability 0 will happen.

(Yes, I know this raises all sorts of difficult issues about real numbers and what it means to choose one at random.)

gregeganSF, to random
@gregeganSF@mathstodon.xyz avatar

Gemini nailing organic chemistry — and also failing it at the same time — by fire-hosing the user with different answers, at least one of which might turn out to be right, even if they all contradict each other.

RobJLow,
@RobJLow@mathstodon.xyz avatar

@gregeganSF Seems to be pretty typical that the H12 (pretty definitive, even if, like me, you last saw organic chemistry in 1978) is used in the first place, but then there's no notion of consistency in the subsequent argument. This lack of consistency is one of the reasons I really don't like this LLM stuff being called 'intelligent'. There's palpably nothing you might reasonably call 'understanding' going one.

AskPippa, (edited ) to random
@AskPippa@c.im avatar

One reason why there can be misunderstandings.

This is the group that made this. https://thinkingispower.com/how-to-speak-science/

RobJLow,
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@AskPippa Though I suspect that at least part of the problem is people disingenuously using the 'public' meaning to undermine the 'scientist' narrative. (See, they admit it's only a theory...)

ColinTheMathmo, to random
@ColinTheMathmo@mathstodon.xyz avatar

I'm hearing that Tony Gardiner has died. 8-(

Tony was amazing ... and he will be missed. Certainly by me, and I'm sure by many others.

Tony was a founder of UKMT and won the WFNMC Paul Erdos Award in 1996.

https://en.wikipedia.org/wiki/Tony_Gardiner

RobJLow,
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@ColinTheMathmo more sad news :-(

ColinTheMathmo, to random
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This is lovely !!

https://www.theguardian.com/science/2024/jan/22/can-you-solve-it-the-greatest-wordplay-puzzle-of-all-time

I've had a go at ScrabbleGrams and they are phenomenally hard for me. I could so easily be nerd-snup by them, so I'm resisting.

But reading some of them impresses me no end.

RobJLow,
@RobJLow@mathstodon.xyz avatar

@ColinTheMathmo I took one look and decided that although I admire them greatly, the attempt to construct one would probably be spending several working days without success, but with a great deal of frustration, so decided against it. (In other words, I chickened out.)

ColinTheMathmo, to random
@ColinTheMathmo@mathstodon.xyz avatar

Ironic that the two o's in 'cooperate' insisted on having their own separate sounds -- https://twitter.com/nathanwpyle/status/1532815303377289216

RobJLow,
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@ColinTheMathmo Harvard has the coop. We, on the other hand, have the co-op.

j_bertolotti, to random
@j_bertolotti@mathstodon.xyz avatar

A sinusoidal Mario

The first few seconds of Super Mario showed as a bunch of moving sinusoidals.

RobJLow,
@RobJLow@mathstodon.xyz avatar

@j_bertolotti Oh, excellent!

christianp, to random
@christianp@mathstodon.xyz avatar

Can whoever keeps trying to reset the password on my Facebook account please not

RobJLow,
@RobJLow@mathstodon.xyz avatar

@christianp @njj4 Or it's somebody using your email address (not knowing that) to try to deal with their own account. Of course, it's you who gets the message. I get it a lot for various accounts that I don't even have.

christianp, to random
@christianp@mathstodon.xyz avatar

For nearly twenty years, my desktop monitor has sat on top of a copy of Kreyszig's Advanced Engineering Mathematics, the thickest and least interesting book I own, to put it at the right height.
My fancy new 4k monitor's stand is the wrong shape to fit on top. The end of an era.

RobJLow,
@RobJLow@mathstodon.xyz avatar

@christianp Now you have to read it.

j_bertolotti, to random
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Any work email you send me during the Christmas break has a 95% chance of never being read.

RobJLow,
@RobJLow@mathstodon.xyz avatar

@j_bertolotti Every work email I send you during the Christmas break has a 100% chance of being read.

rmathematicus, to random
@rmathematicus@historians.social avatar

A Retro-Review: The Sleepwalkers: To read or not to read that is the question?
https://thonyc.wordpress.com/2023/12/20/the-sleepwalkers-to-read-or-not-to-read-that-is-the-question/

RobJLow,
@RobJLow@mathstodon.xyz avatar

@rmathematicus I was taught that Newton used (not developed) calculus to work out planetary motion, but presented it using Euclidean geometry because he thought nobody would accept the calculus based arguments. Is there any evidence for (or against) that?

ColinTheMathmo, to random
@ColinTheMathmo@mathstodon.xyz avatar

Quote:

"Let me emphasize this: inmates took advanced math just for fun."

https://www.ams.org/journals/notices/201911/rnoti-p1821.pdf

RobJLow,
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@ColinTheMathmo So prison inmates are remarkably like professional mathematicians in that respect - maybe more like them than a lot of maths undergraduates...

RobJLow,
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@ColinTheMathmo Yeah, I know. But I used to get a bit depressed teaching modules where the vast majority of students on them just wanted to learn how to pass an exam, rather than learn some maths.

Which is really a problem with the system they were operating within, to be fair - they were behaving perfectly rationally.

And I keep having to remind myself it was just the same when I was a student: those of us who were studying maths because it was fun (with potential benefits for future employment) have doubtless always been the outliers.

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

The headline screams

"𝗦𝗶𝗻𝗴𝘂𝗹𝗮𝗿𝗶𝘁𝗶𝗲𝘀 𝗱𝗼𝗻’𝘁 𝗲𝘅𝗶𝘀𝘁,” 𝗰𝗹𝗮𝗶𝗺𝘀 𝗯𝗹𝗮𝗰𝗸 𝗵𝗼𝗹𝗲 𝗽𝗶𝗼𝗻𝗲𝗲𝗿 𝗥𝗼𝘆 𝗞𝗲𝗿𝗿

What's up with that?

As usual, it's less of a big deal than it looks. But Kerr is smart: he's the guy who first found solutions that describe rotating black holes. And the article is nice and clear. So it's more interesting than the usual nothingburger we've come to expect from screaming headlines about fundamental physics.

Kerr is talking about Penrose's famous singularity theorem, the one Penrose won the Nobel prize for. This says roughly that if space is infinite in extent, and light becomes trapped inside some bounded region, and no exotic matter is present to save the day, general relativity predicts that either a singularity or something even more bizarre must occur.

Of course I'm not stating the theorem precisely here. Each of the vague terms I just used must be made precise. But what's Kerr claiming?

Kerr isn't claiming Penrose's result is false. Instead, he's doing two things.

First, he's pointing out that the definition of "singularity" used in the theorem is not the only definition possible. A "curvature singularity" is - very roughly - a place where the curvature of spacetime approaches infinity. But that's not the kind of singularity that Penrose was talking about! Instead, he was talking about a place where the path of a particle can suddenly end. This may or may not be a curvature singularity.

This is not news.

Second, Kerr is arguing that rotating black holes have some singularities in Penrose's sense that aren't curvature singularities. Unfortunately this argument seems to be wrong.

(1/3)

https://bigthink.com/starts-with-a-bang/singularities-dont-exist-roy-kerr/

RobJLow,
@RobJLow@mathstodon.xyz avatar

@johncarlosbaez @Diffgeometer1 I found it particularly strange that he says in the abstract that Hawking and Penrose just claim that an incomplete geodesic must end in an "actual" singularity, when in fact they are careful to point out specifically that they don't claim the geodesics end at a strong curvature singularity. <shrug>

RobJLow,
@RobJLow@mathstodon.xyz avatar

@johncarlosbaez @Diffgeometer1 I tried, but to be honest I found it really hard going. For somebody complaining about other peoples' assertions, he seemed to make an awful lot of his own, and too much of it just came across as crotchety (at best). I have no doubt his computations are correct, it's what he says about them that is really hard to follow. (And the singularity theorem proofs have been looked at by people much more careful than me without anybody pointing out lacunae.)

I'm mostly now waiting for the dust to settle, and trying to to dig myself into any holes about it...

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