llamaz

The post you're responding to is ambiguous, and most language is and relies on context, but this doesn't seem like a very charitable interpretation.

I have heard the argument you're making with Jordan Peterson (who I absolutely don't respect - if you're looking for a Christian conservative try Peter Hitchens instead, although I'm not a conservative myself. He's not fashionable these days, but he represents actual long standing conservative beliefs rather than opinions that will fade away in 2-3 years)

I think the parent comment is being deliberately ambiguous in order to skirt around politically sensitive issues.

I've taken courses is probability and topology where the power set is used, and am intimately familiar with it, but I have no idea what you're talking about

I'm genuinely curious, how do you think this worked?

https://en.wikipedia.org/wiki/Revenue_Act_of_1935

He doesn't have a particular view on determinants, I got my views on determinants more from Axler than from Halmos. But Halmos' book is linear algebra as preparation for functional analysis, so he tends not to choose a basis for proofs.

I agree with you, that in practical paper computations (e.g. on exams) that determinants are an indespensible practical tool.

I'm vaguely familiar with Axler, but I read the beginning of Halmos (finite dimensional vector spaces)

As a practical example of what I would prefer be taught on the undergraduate level to e.g. engineering and physics majors:

https://www.amazon.com/Vector-Calculus-Linear-Algebra-Differ...

math majors would probably supplement this with additional material

I did degrees in both math and engineering, please give me the benefit of the doubt that I'm not making a 1st year university level mistake.

In the specific examples you give, 2-forms could be introduced instead to yield the final formula for the Jacobian. I don't think this is an overkill, because it's possible to use 2-forms without precisely proving the theorems etc about them. This is more convenient for math/physics people, and engineers care more about the final formula than about how exactly it was derived.

As another comment here pointed to, the idea that linear algebra is better off without determinants was popularized by Axler - I'm not making this opinion up out of nowhere.

That's one concrete way to view determinants, but it's not _the_ way to think about them.

Determinants are kind of abstract and even inelegant. This is because it's defined in terms of coordinates rather than abstractly. A coordinate free definition exists, but it's very complicated.

Ideally they would not be taught at all, but it's useful for doing exam problems. Cramer's rule in particular is quite useful when solving simultaneous equations in engineering under exam conditions, for example. Even in computer/engineering applications, row reduction/diagonal normal form type are used instead.

Determinants are a way to get a scalar number out of a matrix. You have linear forms, bilinear forms, and multilinear forms, the latter of which determinants fall under.

There are certain properties you would like the determinant to satisfy, such as det(AB) = det(A) det(B), so that the determinant can give you an idea of whether a matrix is invertible. Eventually you work out that a determinant _has to be_ a multilinear form with certain properties (alternating, skew symmetric).

Again this is all very complex and messy. Initially 'linear algebra' was just the study of determinants, because people thought of math in terms of solving equations. Linear algebra, as it's known today, came later.

Bilinear forms turn up all the time, so ideally you would first learn bilinear forms, then learn the properties a bilinear form can have (e.g. alternating, skew symmetry, etc), and then learn determinants in that context.

If you're taking a class with proofs, you're being prepared for research. Doing your own research into, and reverse engineering, proofs is an important skill.

Proofs in math journals are given 'as-is' and you learn the intuition through social means and discussions.

In an era of open access journals, and a circumstance where the vast majority of PhD students don't end up gaining an academic job, perhaps its time to both drop the convention that lecturers research and researchers lecture.

The state will have to play the role in funding individual research, since private institutions may want to keep knowledge to themselves as a competitive advantage, or otherwise would be unwilling to fund research e.g. in the humanities.

Historically research was not necessarily a job, let alone a job incentivized by how many papers someone churns out.

Sometimes, like in the case of Spinoza, research was done in someone's spare time while they worked a non-time consuming job (lens grinding). In other cases lecturers, such as Adam Smith, published very little and instead focussed on teaching.

I have no desire to defend the Soviet Union, but out of curiosity, do you think our current system rewards productivity? I'm thinking along the lines of the movie "Office Space".

I don't know much about the USSR, but I don't think they set everyone's salaries the same or distributed money equally, or any other nonsense like that.

I agree, DU munitions are not illegal. Weapons that cause unnecessary suffering are illegal. The question is whether DU munitions cause unnecessary suffering, and whether the US knew that the caused unnecessary suffering.

Ultimately the question is not of great importance because no one actually enforces international law.

Have a nice day :) (said sincerely, without irony)

My position is that the United States should de-escalate an arms race. I don't want to argue about details from examples that I use to support my point.

If you want to labour the point, here's the specific law: https://ihl-databases.icrc.org/customary-ihl/eng/docs/v1_rul...

I'd consider birth defects to be "unnecessary suffering" (this exact wording was used in the Guardian article).

The topic is elaborated on here: Here's an additional link: http://www.austlii.edu.au/au/journals/VicULawJJl/2015/6.html

It's possible to google the answers to these things, and we're getting off topic. Here's something I found that may answer your question:

https://www.theguardian.com/world/2014/jun/19/us-depleted-ur...

I'm not defending Mao or Stalin. I'm critiquing utopian thinking, including that of Mao and Stalin. Communists pursued a utopia, and neoconservatives are pursuing their own utopia modelled on Chicago school economics and liberal democracy.

We should pursue a non-interventionist foreign policy and not force our way of life, which itself is a compromise between different groups, onto other countries. Other countries need to come to a different modus vivendi compromise between themselves and with us, and have as much right to sovereignty as we do.

I'm claiming the united states, in contravention of international law, used depleted uranium [1] as a weapon, and this depleted uranium is causing birth defects. We're getting side tracked, but you can do your own research on this topic and come to your own conclusions. The wikipedia page below is a good place to start.

[1]: https://en.wikipedia.org/wiki/Depleted_uranium

No, I'm an Australian citizen. Yes, I have heard of all of those.

The world does not want "freedom, and democracy", or any ideology that has been used to destroy their countries. The use of illegal radioactive weapons in Iraq is resulting in deformities to this day. (e.g. here's the first link I could find: https://theintercept.com/2019/11/25/iraq-children-birth-defe...)

The Russians do not want a Western model of democracy, especially after the "shock therapy" that sent nationally funded industries into the private tyranny of oligarchs.

Read John Gray. True liberalism means "modus vivendi" politics, reaching a peaceful co-existence with other countries, rather than trying to change the world to realize some sort of utopia.

The communists tried it, the neoliberals tried it. In each case the results have been disastrous.

The US is actively supplying funds to Saudi Arabia, which is culpable for the Yemeni famine. Reading the wikipedia page of the Yemeni famine is enough to establish which country is culpable for it.

Even if Iran is partly culpable, the US is not supplying funds to Iran, and is in fact sanctioning it (incl. medical supplies) during a global pandemic. I mean look at the military bases around Iran alone: https://i.redd.it/2x46rg6uid631.jpg

The current Iranian regime came into power as a result of a US coup of a democratically elected prime minister for the benefit of British oil. China doesn't even come close to the US foreign presence.

It seems to me that the United States is more likely to be the aggressor given its record of interventionism, not to mention Hiroshima and Nagasaki. The Russians and the Chinese are far more peaceful - they do not position military bases aggressively around the world, do not fund proxy armies, and do not fund countries like Saudi Arabia that are responsible for the ongoing Yemeni famine (I've refrained from touching the more contentious topics in US foreign policy). The idea that the United States is under threat, rather than the threat, is laughable.

If any country is well positioned to de-escalate a nuclear arms race, it is the United States, and this is the action that it should take.

I don't know anything about representation theory, but the way you describe it I thought "how's this different from a homomorphism." All elements of a group (e.g. any x, y in your example), are invertible by the definition of a group.

The wikipedia sentence definition makes more sense to me: "a "representation" means a homomorphism from the group to the automorphism group of an object"

This seems natural, since if you take _any_ algebraic structure (e.g. a ring), then its automorphism group is a group. Which is a reason why group theory is worth studying - since _any_ algebraic structure can be studied using group theory by considering its automorphism group. (Also, an automorphism group is just the set of symmetries, so group theory can be described as the study of symmetry).

Check out whitehead’s process philosophy. Deleuze has something similar.

Social democracy is still fundamentally capitalism. Adam Smith was a left-wing radical living in a transnational period period between feudalism and capitalism where the main Tyrannical force was the state - now that has changed to corporations.

Whether you're left or right wing economically, it's an accepted fact that capitalism has a cycle of boom and bust built into it. Right-libertarians (e.g. The Democrats and The Republican Party) believe that this can be avoided by freeing the market by removing deleterious incentives, centrist Keynesians (e.g. FDR with the New Deal, Bernie Sanders) don't trust capitalists to self regulate and instead accept the cycle of boom and bust, but try to avoid the social unrest by smoothing out and mollifying the crises, and left-libertarians (e.g. John McDonell, Richard Wolff, Paul Cockshott) try to eliminate the cycle of boom and bust, much like the right libertarians.

This framing (e.g. of Democrats as economically right) may be provocative to Americans, but is natural in the rest of the world. I'm Australian and Bernie Sanders is to the right of our right wing party.

Currently with Maxwell's equations you can point to each one and couple it with an experiment.

If you simplify the equations any further, it will be a result of mathematical elegance rather than fundamental undergraduate-level physics.

That's true, but I suspect the aspects that math can't model are either known to be intractable problems (e.g. modelling turbulence, Navier-Stokes), or otherwise have been delegated to other fields like philosophy or the humanities.

So I don't think there are physical aspects of reality that we are missing out on because they cannot be modeled using math.

However, the social and historical aspect of science is undoubtedly incredibly important, as well as the selection of the scope of science. These aspects of reality might be underrepresented.

To be more concrete, perhaps in 50 years we'll have doctors who specialize in "suburban salaryman kidneys," because the scope of study will expand from just the internal organs, to the internal organs, together with the external environment and social conditions.

We're already sorta there. A physiologist would conduct research on specific organs and systems, while a general practitioner/family medicine doctor takes your history (i.e. considers the social and historical conditions that lead to illness)

I have tried this, and tt's a good pedagogical method for learning-how-to-learn, but it's inconvenient in practice

I think it's worth learning how to use Anki instead. The key challenge there is selecting the right level of coarseness, so that it doesn't take forever. Even if you don't end up reviewing your cards, the act of synthesising information helps you learn it. Down the line you're able to encode important information in finer detail.

Contrary to what you might think, this method is especially useful for really difficult concepts (e.g. in math and physics). Sometimes you sit through a lecture and have no idea what's going on until you start doing the exercises. In these cases you might have to use memory as a crutch, to try to memorize the main ideas (or useful facts) to create the scaffold which you fill in later.

Consider the example of a highway robber that holds you up at gunpoint and asks for your wallet on the threat of death. In this situation there is typically consent by the victim in handing over her wallet to the perpetrator - after all he has the _free will_ not to hand over his wallet.

In the same way, you have the _free will_ not to work, but the consequences of not working are ending up on the streets. As a special case of this, a prostitute has the free will not to work, on the threat of ending up on the streets. The only difference between a generic worker and a prostitute is that it is the human reproductive act itself that is being commodified.

I guess that the question of whether prostitution is exploitative or not, and whether generic work is exploitative or not, depends on what _alternative_ choices are available: Does society guarantee that you will not end up on the streets i.e. (1) is there a scarcity in the basic human needs of society, viz. housing, jobs, the recognition in law of that someone is a citizen etc. (2) does society provide these basic needs to all its members.

From this framework it's possibly to argue that _in principle_ prostitution is exploitative. It is no more exploitative than any other form of work, but perhaps has a tendency to attract the most vulnerable in society who do not have a safety net to fall back on. So I don't see anything especially exploitative about a middle class woman becoming a stripper to get through college. But not everyone is middle class.

What's undeniable _in practice_, is that legal prostitution leads to less criminal behaviour and exploitation. Hopefully we can work to change the conditions that make prostitution exploitative as opposed to an expression of an individuals creativity.

There is some truth to the theory of "cultural Marxism" but it's usually presented in an unflattering and conspiratorial light.

Gramsci, a prisoner of Mussolini, questioned why Marxism had failed to foment revolution in the west. He came to the conclusion that the working class were indoctrinated, and that a "counter-hegemony" of thought based on progressive values was necessary to grow a more egalitarian society.

Herbert Marcuse, perhaps the defining philosopher of the 60s, continued this line of thought. There was no conspiracy or deception, however, since Marcuse was an open Marxist. He had a significant impact on the radical culture, and the sexual revolution of the 60s.

In this sense, if you are opposed to "cultural Marxism," then you are opposed to the cultural shift of the 60s. Personally, I think the cultural shift of the 60s is to be celebrated.

We're right in the West to reject Leninist ideas, but it's important to understand the historical context in which Leninism gained traction.

Russia was a backwards pre-capitalist third world monarchy with vast economic inequality under one of the richest men in all of history, Nicholas Romanov II. He rejected attempt after attempt to reform his monarchy into a democratic constitutional monarchy, preferring to cling onto absolute power and repeatedly losing wars. The story of the Russian revolution is one of a transition from authoritarian rule to authoritarian rule.

Initially the revolution was widely praised by genuine revolutionaries, such as Kropotkin, Emma Goldman, & Rosa Luxemburg. The country was ruled democratically by a system of workers' councils (soviets), and workers were encouraged to form committees to self manage the work place democratically.

Within the year, however, the Soviets were dissolved and commissars were sent to the factories to take the place of the boss', effectively ending workers' self management. This was widely condemned by mainstream Marxists, most notably Rosa Luxembourg, who sent a historic admonitory letter to Lenin. This is when the idea of "Marxism-Leninism" as opposed to simple "Marxism" began to distinguish itself.

What Leninism has become now is a sort of paranoid ideology about "holding onto the revolution" against "the forces of reaction." They point to examples of successful workers' self management e.g. The Paris Commune, Anarchist Catalonia (read "Homage to Catalonia" by George Orwell), and claim that these revolutions were crushed because of a lack of "party discipline" and organization.

I’m not sure what wealth is. Let’s use the term value i.e. when raw materials (eg ones and zeros) are transformed to a useful form (eg a computer program). The programmers at amazon create value and then use most of their wage on subsistence eg supporting their family. The board of directors buy, ultimately through a chain of command, workers who are able to make more value than they consume in wages (otherwise no one would hire her). They also use money for subsistence, but they consume part of their accumulated value on creating more value. The programmer takes risks in agreeing to work, because if he is layed off then he won’t be able to provide for her family. So how can the programmer also use value to create more value? Entrepreneurship, ie being paid based on the profits she generates, rather than what the board of directors is willing to let go of. Or perhaps investment, which ultimately means profiting off the value creating labour of others in a indirect way.