You think the national GOP is bad, look at the Texas version:

The new platform would call for:

Requiring Texas students “to learn about the humanity of the preborn child,” including teaching that life begins at fertilization and requiring students to listen to live ultrasounds of gestating fetuses.

Amending the Texas Constitution to remove the Legislature’s power “to regulate the wearing of arms, with a view to prevent crime.”

Treating homosexuality as “an abnormal lifestyle choice,” language that was not included in the 2018 or 2020 party platforms.

Deeming gender identity disorder “a genuine and extremely rare mental health condition,” requiring official documents to adhere to “biological gender,” and allowing civil penalties and monetary compensation to “de-transitioners” who have received gender-affirming surgery, which the platform calls a form of medical malpractice.

Changing the U.S. Constitution to cement the number of Supreme Court justices at nine and repeal the 16th Amendment of 1913, which created the federal income tax.

Ensuring “freedom to travel” by opposing Biden’s Clean Energy Plan and “California-style, anti-driver policies,” including efforts to turn traffic lanes over for use by pedestrians, cyclists and mass transit.

Declaring “all businesses and jobs as essential and a fundamental right,” a response to COVID-19 mandates by Texas cities that required customers to wear masks and limited business hours.

Abolishing the Federal Reserve, the nation’s central bank, and guaranteeing the right to use alternatives to cash, including cryptocurrencies.

When I was a kid in Texas I would wear my cowboy hat and shoot my cap pistol while singing, "The eyes if Texas are upon you . . ." :roll:

I don't think you can pull of such a stunt in the so-called hard sciences — Agent Smith

Not exactly a stunt, but close:

The Bogdanoff Affair

I seem to have missed this thread when it ran seven months ago. Kenosha Kid gave some good answers to questions about recursive vs iterative. I usually think of iterative as involving the same function in a loop, like fractals, but I suppose the following, which I have explored extensively, might be considered iterative. Maybe not. It makes no difference what it is called, although I refer to it as infinite compositions.


${{g}_{n}}(z)=z+{{\rho }_{n}}{{\varphi }_{n}}(z)$

${{G}_{1}}(z)={{g}_{1}}(z),\text{ }{{G}_{n+1}}(z)={{g}_{n+1}}({{G}_{n}}(z))$,
$n\to \infty$

What astonishes me is the godlike status these parties are afforded such that any policy they come up with is waived through as being at least reasonable, but every alternative is treated as if it were utter madness. — Isaac

:up: I despise policies set forth on the far right as I despise those set forth on the far left. Where is the middle these days? I'm dropping a party affiliation and going independent.

And before that, Moses said that, and before that, Kain said that. — god must be atheist

My advisor said that regarding mathematics a half century ago. Didn't buy it.

↪jgill
Are you rolling your eyes or wagging your finger at me? — unenlightened

I love the poem, but beyond that is the fact that Khayyam is an academic ancestor of mine, having written about mathematical continued fractions - a topic I've researched.

Not about common ideas. Pretty straightforward. If you quote someone, cite the source — Jackson

:up:

The moving finger wags, and having wagged, moves on

:roll:

The Moving Finger writes; and, having writ,
Moves on: nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.

"The Rubaiyat" by Omar Khayyam (Fitzgerald translation I think)

Journals are overflowing, so the possibilities of mistakes and intentional deceptions is fairly high. In math it's impossible to keep up with new subjects (24K on Wikipedia). Although I continued doing research I gave up on publishing over twenty years ago, thinking, Why go through the sometimes lengthy procedure when only a few people in the world are interested (and I had gone through the promotion processes years before)? There's a tremendous amount of scholarly clutter out there.

Two comments that really prove nothing:

1. I took over a 5.25% mortgage when I bought a house in 1972 and the going rates were 8% - 9%. I was told "You'll never see such a low rate again!" When I had a house built in 1985 I was fortunate to get a 15 year VA loan at 11.25%.

2. On both occasions when I received checks for over $2K from the government during the pandemic I thought, Why did they send me money I don't need? I suppose that it cost more to differentiate needs than to simply send blanket $$ out.

Friedman was at the U of Chicago when I was there, but I never met him. :nerd:

I don't see the other possible cause: The federal government printing and giving away too much money.

An infinitesimal monad attempts to gain substance by adding itself to a number . . . . but fails

5+m=5

:cry:

The wedding of two monads: m+m=m

Born into the prevailing religion. But over two millennia ago it offered a kinder, gentler God than the brutal gods of the time. Also, it garnered support from the ruling class since it referenced "Caesar's coin". Too complicated a subject for simple answers.

I find this quote from wiki to be interesting:

In fact, a theorem proved by Phillippe Eberhard shows that if the accepted equations of relativistic quantum field theory are correct, it should never be possible to experimentally violate causality using quantum effects.

This is all physics and a discussion between two people. It's admirable, but why not on the lounge?

The Less-is-more effect is a positive outcome of heuristics, which itself is a small part of the very large cognitive bias spectrum. Math people use heuristics all the time to uncover general truths before looking for proof structures. However, it fails in this regard frequently. I just finished using it to define a specific outcome, only to discover a fallacy upon closer inspection.

I'll speak to mathematics publications. First, open access journals are no more legitimate than the several large academic posting sites, including ArXiv.org and researchgate.net , where authors can present papers either before or after publication in refereed journals, or preprints that may not even be submitted to these journals. To join these sites requires some minimal academic credentials, however. And the sheer number of legitimate articles is overwhelming. ArXiv.org receives 140 - 250 papers a day, 365 days a year.

Most open access journals are there to make money, not guarantee accuracy. My guess is that no credentials at all are needed.

Even highly-regarded journals print duds from time to time. In math, sometimes the referees are a little lax and let results reach print that are simply not valid. This can happen when the article being examined is by a known colleague who is respected. Or a paper far out of the mainstream, so that it has little to no importance to the larger community, and the referee would rather be doing something else. Usually referees are volunteer academics who get no extra pay for their services, but their institutions show their appreciation in release time or whatever.

My take on the whole situation is that "fake academic news" is way more prevalent in publications in the humanities, where the sheer volume of words, some of which are poorly defined, may provide opportunities for intellectual contamination. Toss in only lightly understood statistics and there goes the ball game.

What I would like to know is how and why people think it can help with critical thinking — Skalidris

When I taught complex variables, a senior level mathematics course, I would resort to heuristics in order to encourage understanding of principles and theory. A theorem might require a complicated proof, but by drawing pictures on the board and describing the underlying concept students could see through the complications and comprehend a rational argument that implied the result. It was a shortcut, but one I have used for myself numerous times. If an idea is abstract and convoluted, find an example that illustrates the idea. Then study the formal approach.

I have no idea if this is the sort of thing you have in mind. Heuristics is in the broad category of CB. I've found that extracting an idea and making it personal in some way helps critical thinking. But I think this thread is more about political biases.

I find the whole idea of cognitive bias unconvincing. Even if it is true, so what? — Jackson

On the other hand, confirmation bias distorts news all the time and is a threat to democracy.

Another common point is that theory guides observation in the first place (tells us what to look for, frames the situation.) — igjugarjuk

I speculate my specialty (infinite compositions of complex functions) is a solution awaiting a problem. :cool:

We want innovation and groundbreaking "new" ideas, but only to a certain extent. — Paulm12

That's what grad schools are for. Although there are some spectacular examples of this from undergraduates and drop-outs, it doesn't happen that often. But you are talking about "small private" schools and I was thinking of larger private schools, like the U. of Chicago where I went for a postgraduate program long ago.

It seems that there are two competing ideas - the idea that education should serve to teach people specific skills to be productive in society and conform, and the idea that education should encourage people to come up with new ideas and think independently — Paulm12

What of history, particularly that of democracy? How does our government work? What of the sciences?

I don't see that the two areas you describe are necessarily in conflict. But interesting thread.

Your last paragraph is inaccurate, however, as I am familiar with both kinds of institutions.

We learn by observing nature. Then we take those observations and extract their essences. — jgill

I'm with you in spirit, but perhaps we dream up those essences and only later learn to check if they or their implications are compatible with observations. — igjugarjuk

In all my years as a mathematician, however, I must confess that I have never worked in applied mathematics. Like most in my profession, I explored an intriguing abstract concept. Still do.

At that point I think we start to take philosophy less seriously — ZzzoneiroCosm

You mean there are those who do take it seriously? :snicker:

It's interesting that the expression, metamathematics , coined by Hilbert a century ago, is much easier to describe than the more archaic metaphysics. Discussions of the former rarely use that term, whereas the latter produces volumes, and still gets nowhere it seems.

Sartre's notion of pre-reflective consciousness as nihilation. This was absolutely new. Historically, no philosopher, other than Sartre, came up with this notion.

I anticipate that there will be many other such future geniuses — charles ferraro

Perhaps you could summarize this idea of Sartre's briefly.

The word metaphysics should be eliminated from discussions of science. It is archaic, like a lady two hundred years ago suffering from the vapors after witnessing a strand of ectoplasm.

In science,metaphysics is an archaic word replaced by speculation in science.

At first glance one might conclude that the masters of generations long past did it all due to the ongoing discussions about those philosophers. On the other hand there are areas like the philosophy of mathematics and the philosophy of physics that are vibrant.

Look at all the babble about quantum theory. And judicial philosophy easily reaches the common citizen with reports of deliberations by the SCOTUS and actions and inactions of the Attorney General.

How can ethics not be on a top burner with the ongoing war in Ukraine, and a philosophy of international relations.

Dynamical systems (causal) can be so complicated that stochastic-correlational is the only way to work with them. Pretty much all it takes are functions that are not invertible.

The computer could be, for example, a huge cellular automaton — Gnomon

Wolfram (creator of Mathematica) attempted to convince the scientific community that cellular automata were at the heart of virtually everything physical. He failed.

As a mathematician who never gave much thought to Platonic ideals, my rather superficial view is that these ideals do not exist in any sort of physical forms, but exist in an abstract space that is accessible to human minds, in much the same way that spaces of functions exist in the normal mathematical realm. Abstractions from reality are commonplace in math.

It seems as if we are more satisfied when we can picture things than when we are left with no choice than write equations — Manuel

You and me both. The math I explore has strong visual components, but not from nature. Patterns in the complex plane mostly. Look at my icon.

:up:

I'm surprised your PhD program didn't have this as a requirement. But, like math, there are many paths to follow.

So much confusion about Quantum theory occurs because those who are not physicists try to take mathematical descriptions (they probably do not understand) and turn them into physical objects.

The wave function is a probability amplitude form that has complex values - not something traveling through space. Superposition arises from a linear differential equation (DE) having linear combinations of solutions, not some mystical process hovering in the aether ready to appear after some sort of magical "collapse".

The concept of "measurement", which we all assume is something like an electronic ruler or scale, seems to be at the heart of understanding QM and has no easily understood definition. Wiki:

In quantum mechanics, each physical system is associated with a Hilbert space, each element of which is a wave function that represents a possible state of the physical system. The approach codified by John von Neumann represents a measurement upon a physical system by a self-adjoint operator on that Hilbert space termed an "observable"

As I have pointed out before, a stripped down version of the Schrödinger equation is nothing more than a very simple DE describing, for example, continuous compounding from your local bank. Somewhere in all of this is the miasma of entanglement, which only God seems able to unravel. :roll:

Sorry, but I think such speculations are ridiculous.

We learn by observing nature. Then we take those observations and extract their essences.