mrjangles

It's just that it is very much a "mathematics for engineers" style course. I think very few of the subjects outlined there give you a flavor for what "real" mathematics is really all about at all (except for algebra, which you do mention).

Apart from the applied stuff you mention, the real core of a mathematics education involves, I think, 4 main areas with significant overlap

Group A: number theory, graph theory, combinatorics

which shares concepts with

Group B: Algebra, Topology, complex analysis, differential geometry, metric spaces...etc

which shares concepts with

Group C: Functional analysis, measure theory

which shares concepts with

Group D: probability and statistics.

As for the applied math that you mention, you should really need to add vector calculus and I'd highly encourage anyone to take a course on fluid mechanics (from a mathematics department instead of an engineering department) to get a real feel for vector calculus in action.

Yep, I came here to say this.

I think it is important that anyone who wants to study math understand that real math is not at all like what you learn in a physics or engineering department. In these departments you will always hear people say things like

>"proofs are not useful, all you have to do is memorize the 'trick' they use. Once you know which trick to use, it is easy"

or you will hear them say.

>"Math isn't about understanding, it is just about learning rules and symbols on paper".

This is not mathematics. These things do happen.... in a physics and engineering department. It is, in fact, a descriptions of a physics education, not a description of a mathematics education.

For this reason I would be careful taking mathematics advice from physicists too seriously as they may, unintentionally, lead you very far astray.

I think what happens here is that Orwell is having a big stab at the intelligencia, and the intelligencia at the time (as now) hated nationalism. He is trying to point out all the ways their behavior is just like that of overzealous nationalists at the time, so he redefines the word so as the label all the intelligencia as the thing they hate.

It makes for effective rhetoric. I think anyone reading this should keep in mind that he seems to have good things to say about what he defines as "patriotism", which is what we would mean by the word nationalism today. In other words, he would absolutely not agree with the anti-nationalists of today who hate their country. In fact, he goes out of his way in this essay to label those people as prime examples of "nationalists".

Last I checked the there were enough free parameters in these calculations to make the calculations of less than convincing. For example those 'hadronic observables' make up such a big part of the actual results that what is left over is within the error bounds anyway.

However, that was over 7 years ago, and someone else in the comments linked an article talking about the breakthroughs since then, and they seem significant, so things may well have improved since then.

Regardless, lattice QCD has always been real science and always been quite impressive. Any direct attempt to match theory with known experiments always is real science regardless of whether you agree with the methods.

Ok good point, I think I got side tracked with my comment.

Perhaps a better analogy would be: Someone who claims to be a chess player, but keeps getting disqualified from tournaments for making illegal moves.

For example, when it comes to QCD and the structure of the nucleus, we have no idea if our theories are correct or even make sense. One of the millon dollar Millenium prizes is currently being offered for anyone that can prove the equations of QCD are even well defined or if it is possible to even have a bound state (i.e for particles to exist at all) within a QCD framework.

So my point is the underlying theory is really only described in the perturbation theory setting. I.e., in the high energy limit (smashing things together). Now the equations and mathematics behind QCD are very attractive and probably contain a great many aspects of what we will eventually become the full theory, but until we can predict, for example, the mass of a nucleus from those equations (or anything at all whatsoever), then they are certainly not proven.

So far all we know is that these equations can predict what comes out (and in what direction) when we smash particles together.

My comment went from, like +10 votes to -1 and flagged in 1 hour.

Is this your doing or someone else?

I also have a PhD in Physics, everyone I know in my field agrees with me, including my professors. Sorry, but disagreeing with me is NOT a reason to be flagging comments. If it wasn't you then the apologies, I guess my comment is for whoever did it.

Back in the 1960s and thereabouts, physicists liked to believe that this was the case. Since then, breakthroughs in our understanding of quantum mechanics and solid state physics has changed that (particularly in things like super conductivity). Today, it is pretty much accepted that the standard model is really, what is called, an "effective theory".

What this means is that we discovered that the structure and order, as we see in particle physics, actually appears everywhere in nature. For example, vibrations moving through a solid (such as when you tap the table in front of you) actually behave exactly like (what are incorrectly named for historical reasons) "fundamental" particles moving through space. They interact with each other mathematically with the exact same equations. Recently scientists even created a material which these "quasiparticles" (as the excitation are called) obey the laws of special relativity inside the solid, except the speed of light is replaced by the speed of sound in the solid.

All this probably reached its peak when the Higgs mechanism, and indeed pretty much the the entire theory between the Higgs particle, was discovered by P.W. Anderson in superconductors. He suggested that perhaps the same mechanism is what gave particles in the standard model their mass. He was proven correct, but the Nobel prize went to Higgs for historical and political reasons, and also because P.W.A already had one Nobel prize.

Now days high energy particle physics views space as a kind of medium, and the electrons and quarks etc as just being the particular manifestation of whatever chaotic thing is going on underneath (more particles or who knows what), which is meant by "effective theory".

Anyway, the point is that no, it isn't that case of a few fundamental rules are controlling everything. We now have a much better picture and it seems to be order and chaos appearing in all different scales in all different manner of ways and to understand each manifestation one needs to start a new each time.

Phillip Anderson's famous article "More is Different" from 1972 was the first to really espouse this point of view. It has become sort of an anthem for many scientists. https://www.tkm.kit.edu/downloads/TKM1_2011_more_is_differen...

Probably the most important part:

>Martin also said NASA is obscuring costs that it is spending on the Artemis program and that, in aggregate, his office believes NASA will spend $93 billion from 2012 to 2025 on the Artemis program.

You need to read the article to understand my comment. It is specifically about the crisis in high energy particle physics and cosmology. My comment specifically mentions advances in other areas of physics. In case it wasn't clear, I am saying these advancements, such as imaging and understanding glass (and quantum computers, semiconductor tech...etc), are currently the edge of science and our understanding of the universe. It is progressing, albeit slowly, it just doesn't get any hype like the pseudo-science stuff does.

Whenever I read any history of European democracies, I always get the impression that political oppression was a lot worse in the past than it is now, despite how bad it may appear.

I've always wondered if Europe's decline into totalitarianism was halted all on its own due to the natural "swinging of the pendulum" as they call it, or if it was due to American hegemony over the world, and the fact they basically had the whole of Europe under military occupation until the fall of the Soviet Union.

Is today's rise of totalitarianism in Europe simply the swinging of the pendulum, or is it due to the waning of power in the American empire, and therefore the return of Europe to its natural, equilibrium state?

But the civil war in the Ukraine has been going on for 8 years, 12k people have died over this time and the shelling has been fairly continuous over this time with only short lived cease fires. So what has been happening is already similar to Yugoslavia.

However, what is happening now is very different. This is more like when the US attacked Libya and it was over in two weeks.

The article doesn't mention, but also one of the million dollar Millennium Prizes is to do with exactly this.

Except for a few very special circumstances (high energy collisions), we can't get any real answers from Quantum Chromodynamics (QCD) about the nucleus that actually agree with reality - we can barely get any answers at all.

The problem is that these equations use what mathematicians, somewhat disdainfully, like to call "formal mathematics". That is to say that they are just a bunch of rules for manipulating symbols on paper that don't really make sense. More like numerology than real mathematics. No one knows if the rules make any sense at all. If you follow the rules in a different order, for example, you get different answers, and no one knows what it means. The "formal" equations are more based on physical understanding and not the usual solidly based "real" mathematics.

It is kind of like how people started using complex numbers before they understood why they worked. They knew the square root of minus 1 was nonsense, and yet you get the right answer, but no one knew why. Today it is a similar situation with QCD (except you can hardly get any answers at all).

So if you solve this problem (either in the positive or negative) you get 1 million dollars.

I didn't believe you so I looked this all up and indeed everything you said is correct. My GR professor was famously one of the worst academics at the department and he never taught us any of that. His specialty was GR too.

Anyway, your response was needlessly hyperbolic. The only two misconceptions you are correcting here is that tidal forces can be quite weak at the event horizon and the universe does not come to an before passing through it.

Here is the article

https://www.cnbc.com/2021/10/05/tesla-must-pay-137-million-t...

relevant line.

“In addition to Mr. Diaz, three other witnesses (all non-Tesla contract employees) testified at trial that they regularly heard racial slurs (including the n-word) on the Fremont factory floor. While they all agreed that the use of the n-word was not appropriate in the workplace, they also agreed that most of the time they thought the language was used in a ‘friendly’ manner and usually by African-American colleagues.”

I'm guessing from these responses that 'singularity' has turned into kind of pop-culture term expressing the center of a black hole.

A singularity is just where physical quantities go to infinity. There are many singularities at the event horizon. For example, as you fall into a black hole and approach the event horizon the time of an observer a distance away begins to speed up and approaches infinity - the universe comes to an end before you actually reach the event horizon. Many unphysical things like that happen. These are all singularities.

Importantly also, the energy density of space-time approaches the plank energy and this is a region where general relativity and quantum field theory do not agree with each other. So we know the equations are non-sense in this region for sure.

This makes no sense. When you apply the mathematics of fluid dynamics to the problem of water leaking through a dam wall, you get singularities.

It makes no sense to say "you either believe the amount of water in a dam wall becomes infinite and the universe collapses in on itself inside a dam, or you have a better theory, what is that theory?" (you would become a famous mathematician if you had that theory by the way).

Einstein and all the great scientists from that era didn't miss black holes, they thought the idea of black holes were stupid and looked down on people doing that kind of research. Freeman Dyson talks about this in a few interviews - though he doesn't seem to understand why they thought that as he personally loved black hole research.

A singularity is, afterall, a mathematical effect that occurs everywhere in science when the mathematics used to describe the system in one region is no longer valid in another. Only in modern, government funded 'science' do we start to find people taking mathematical errors seriously. Also, to preempt any responses I might get, no, massive dark objects at the center of our galaxy are not even close to being evidence that space-time singularities are real.

And tell me, what do you think would happen if they started building wind turbines in the middle of cities? There is no reason you couldn't fill Central Park in New York with them. Maybe put one on top of every building? You could have thousands of huge turbines powering every city.

I wonder why no one ever seems to suggest that?

Oh wow my mistake. Yes it is actually the sequel "what do you care what other people think" that was written after his death.

Yeah knowing he wrote it, I guess it does come off a little more egotistical than I at first assumed. Still a good book though.

Ok maybe I was being overly hyperbolic before, but the facts here are clear:

The CCP used people in Australia to get close to, and pay off, politicians who they thought would be inclined to favor their cause. Every single one of them belonged to the Labor party. I don't think anyone can call this spin, and I don't think any honest person would doubt that the media would be going absolutely bananas right now if all these people were Liberal party. Hell, they even tried to smear a Liberal party politician as a Chinese spy simply because she was a member of an overseas student club, that is how low they would sink.

As for Stan Grant, he has been approached multiple times by both the National party and Liberal party to run for parliament with them. He was then put into the ABC by Ida Buttrose after she came to the ABC with express goal of evening out the extreme left wing bias at the ABC. His purpose at being at the ABC is literally to give a different perspective to their usual stuff.

As for the ABC and Guardian, they are constantly pushing their audience to believe that democracy is deeply flawed. They are also constantly talking about what an amazing economic system China has and that their model is the way of the future. The only reason they are anti CCP in particular is because the entire word-wide left turned anti-China back in January 2019 overnight.

for some reason, a great many people on the internet don't seem to understand that it is not "his book". It was written after his death by his friend.

I don't suppose you know how to search your own comments do you? I could find it for you if you really wanted because I commented on it the last time it was on the front page (quite a long time ago). I would need instructions on how to search though, no way I could scroll that far back.

>spinning this to claim that the Labor party are friendly to China.

Sorry but this is ridiculous. The Labor party are openly friendly with China, this isn't some kind of spin. Not only that, but their supporters in the left wing media are even more so.

If anyone doubts that, have a read of this article from the main left-wing news site in Australia that is, no joke, trying to spin this into a story about anti-vaxers working with the Russians to interfere in the election.

https://www.abc.net.au/news/2022-02-10/russian-agent-suspect...

Just in case anyone was in doubt of how despicably dishonest this particular source is, you should definitely go ahead and read this.

Edit: wow, and at the end they even try to imply that anti-vaxers are involved with the Russians (with carefully chosen weasel words of course).

>Tesla's Fremont factory is a racially segregated workplace where Black workers are subjected to racial slurs....

This article doesn't say it, but the last time this came up, in small print, it was admitted that all reported instances of racial slurs were delivered by black people to other black people in a friendly manner.

17% of people under 30 have been in a committed relationship with someone they met online, ever (gets lower with age too)

https://www.pewresearch.org/internet/2020/02/06/the-virtues-...

of those with a partner, 21% said they met them online (gets lower with age too)

https://www.pewresearch.org/social-trends/2020/08/20/nearly-...

And note that this says "online dating" not specifically tinder. Statistics show that 80% of women sleep with 20% of men on Tinder. Tinder is a place women go when they are interested in having sex with men based on nothing other than their looks. That is fine, if you are in the top 20%, if you aren't, it is a real fools errand.

I've never seen a libertarian go to the grocer and demand that he be given food for free.

I mean, you would have to read a history book written before 1980 when it became popular to start rewriting history. But a quick search comes up with this for example

https://thewire.in/caste/caste-history-postcolonial-studies

I remember reading a very long time ago that someone did some research on this very subject and found that the majority of problems go away if you don't deal with them. They concluded that this could be part of the reason procrastination exists - procrastinators had a genetic advantage in saving a lot of energy.

This is the usual rewriting of history. It is an extremely modern trend to try to blame the caste system on the British. The British weakened but tolerated the caste system because there would have been immediate revolution had they even thought about removing it. The British were also firmly nationalists who believed that foreign cultures had the right to administer themselves in the way they saw fit.