That question is floating in the air for me. Why do you ask it? — Tom Storm

If there is conflict between academia and the non-academic world, there is assuredly meritocracy in the former within disciplines, leading to personality if not funding squabbles. Sometimes those involved might assuage their feelings by displaying a touch of arrogance towards the less educated. This is unfortunate, but occurs occasionally. It's not pretty. On the other hand, higher education itself does not lead to meritocracy in a more general population since standards vary significantly across the globe. Just a few random thoughts.

In 1951 they didn't need to ask themselves, "Will x news headline cause anxiety and depression?" because maybe only thirty percent of people in the neighbourhood even read the newspaper on a daily basis. — kudos

Long before that defense pundits and military planners carefully manipulated news media to support the war effort. And perhaps not everyone read a newspaper, but almost all listened to the radio.

In a larger sense, is a meritocracy unfair?

↪Athena
Well then somebody ought to hurry up and tell the Scandanavian / Nordic countries that they've been doing their brand of welfare-state capitalism wrong for almost a century. — 180 Proof

Is There a State Crises in Sweden?

Food for thought. Balancing a welcome carpet for immigrants with social welfare movements. Law and order issues. And more. Sweden's wealth distribution figures are similar to those of the US.

If you attempted to apply the idealized structure of mathematics to physics problems you’d encounter unexpected results because the real world doesn’t always deal in easily determined discrete quantities — kudos

In a sense calculus has an "idealized" structure and physics cannot do without it, but you must be referring to set theory and foundations, and the axiom of choice, and the physics I am barely acquainted with does not require the latter.

The academic may know a lot, but they don't know how to truly behave like a layman. They can never know how to not know what they know, and that is a weakness — kudos

This sounds like an argument an anti-vaccine layman might make. Pity the poor virologist who toils in the lab.

:up:

I can add little to nothing. You have expressed your point of view - to which I agree - admirably.

Assuming work is required for most - yes, a dreadful indignity of the human spirit - should a country, say the USA, make a top priority a minimum wage for any job must be enough for an individual to survive on their own - food, lodging, transportation, etc.?

A beginning worker at McDonalds would not be forced to live at mom's home or share expenses with another for the necessities. And more men in the US age 30 and below do in fact live at their parent's home than was the case twenty years ago. More young women, too.

Belonging to a much older generation I still believe in working one's way up, but housing is out of sight these days and gas is $3.50 - $4 a gallon. Prior to this three generations might live in the same house, and I see this returning, along with multiple families in one home.

Why stop at open borders? If someone lives in the US, shouldn't they be allowed to vote - especially since they pay taxes? I bring this up as devil's advocate.

Scientific speculation is when two physicists discuss entanglement. This becomes philosophy when
one of them mentions Kant.

This is the best description of the truthiness of Euler's Identity I could muster. I didn't refer to any math textbook, nor did I consult a mathematician, the equation seems/feels true. — TheMadFool

Amazing. If mathematical life were only so simple. :roll:

As I might practice it, it's speculation. However, the literature shows that is a specific formal philosophical pursuit.

Using as few words as possible is just as important as using the right words. Your argument could have been a lot clearer, less ambiguous, if you'd made the post a lot shorter. — T Clark

Philosophers love using words, the arrows in their quivers. And some, perhaps most, enjoy reading lengthy treatises. As an olde math person I admire brevity and conciseness, so, like T. Clark, I failed to make it through the OP, which, nevertheless, seems very well-written.

The premises of many philosophical efforts frequently seem vague, to the point where, for example, the word "being" triggers my full retreat. "Metaphysics" also is confusing, and I am curious what Stanford's metaphysical laboratory can produce as enlightenment. Mostly it's just me.

I only recently got a smart phone, but I don't use it much. Those damn small letters and having to move the text in order to read it. Nah. — baker

Fat fingers is a drawback. I try to avoid apps, but it keeps wanting them. Very demanding. :angry:

Einstein's Special Relativity applies to physical objects. But General Relativity includes the subjective observer in the network, as a node in the whole pattern, by taking a god-like perspective, from outside the system looking in — Gnomon

I think both special and general include observers. That's not the usual distinction. Accelerated motion and other features are considered in general.

Well, as an elder - perhaps the elder at age 84 - on this forum, I'll make a few comments. But first, anyone older than me please speak up.

They probably don't feel physically like age 25. When I say I feel young, I mean mentally, but what do I mean by that?
— Bitter Crank

• Active curiosity (Important as one ages. Don't give up on the world.)
• good memory (I wish. Images pop right up, but words describing them don't.)
• ability to concentrate (Hopefully you've honed this over the years. If not, good luck.)
• better intellectual skills - less overall stupidity (In politics recall what W. Churchill had to say about liberalism vs conservatism)
• much more perspective (Depends if you've paid attention when younger.)
• Sex drive at 75? Mercifully lessened (Speak for yourself, buddy!)

.

I wonder how the making of concrete and steel will be powered? — Xtrix

Evraz steel mill in southern Colorado is constructing a massive array of solar panels to be the first steel mill in North America to incorporate solar power. This is nothing short of amazing. It's about fifteen miles from where I live.

Mr. Coal, Manchin, will be lobbied to take this out — Xtrix

I wonder how the proposed desalinization plants for coastal California will be powered?

I know it's trite, but imagine a maleable plastic doughnut being continuously deformed into a coffee cup. The notion of continuous transformations from one object to another is the fundamental topological characteristic. The more technical aspects involve open sets. If X is a non-empty set, a class T of subsets of X is called a topology on X provided (1) unions of sets in T are sets in T, and (2) intersections of finite collections of sets in T are sets in T.

The study of topology begins with point-set topologies - and I have fond memories of being introduced to these in 1962 and teaching them during the last quarter of the past century - and proceeds to esoteric terrains I dare not tread.

As G. F Simmons said, "A topological space can be thought of as a set from which has been swept away all structure irrelevant to the continuity of functions defined on it".

One reason I wished to discuss the senses, specifically taste and smell, was they appeared to be qualitative (nonmathematical) instead of quantitative (mathematical) — TheMadFool

Qualitative does not imply nonmathematical. For example, it used to be said that topology is math without numbers, although that's not entirely true.

You seem to curiously relate politics to theology to mathematics... why though is beyond me, creating some odd mathematical mysticism that you seem to want our kids to learn — Tobias

Good point.

That is speaking of the "one is the many" as monad means one and is represented as a circle. — Athena

I had not thought of monads apart from Leibniz's mathematical contributions. I now see that there is much more to the monad than I knew. Thanks for bringing this up. :cool:

From lecture notes by Sourav Chatterjee, Stanford:

Although quantum mechanics has been successful in
explaining many microscopic phenomena which appear to be genuinely ran-
dom (i.e., the randomness does not stem from the lack of information about
initial condition, but it is inherent in the behavior of the particles), it is not
a good theory for elementary particles, mainly for two reasons:

• It does not fit well with special relativity, in that the Schr ̈odinger
equation is not invariant under Lorentz transformations.
• It does not allow creation or annihilation of particles.

Since in lots of interesting phenomena (e.g., in colliders) particles travel at
speeds comparable to the speed of light, and new particles appear after they
collide, these aspects have to be taken into account.

Quantum field theory (QFT) is supposed to describe these phenomena
well, yet its mathematical foundations are shaky or non-existent. The fun-
damental objects in quantum field theory are operator-valued distributions.
An operator-valued distribution is an abstract object, which when integrated
against a test function, yields a linear operator on a Hilbert space instead
of a number.

Losing yourself in a flow state doesn't mean shifting to another "self". It means becoming part of the process without one's ego. That's a problem with philosophy, which involves thinking rather than doing.

The second paragraph here is a good description: Generalized functions. I've never worked with these things. Continuous linear functionals are called distributions, also. A linear functional takes a function in a function space and produces a number (real or complex). For example, in the space of complex contours the length of a contour is one such functional.

The flow state was popularized by an old acquaintance of mine, Mihaly Csikszentmihalyi. In the sport of rock climbing it can be a delightful experience as long as difficulties remain mild as felt by the climber.

Entanglement frequently arises in these discussions, and it's tempting to wander into quantum mysticism. Here is a fairly clear-eyed perspective of it, from Quora by Mark John Fernee:

It's the quantum version of a correlation. That means that two or more parts of a quantum system have correlated properties. What's strange about it is that the correlation is indeterminate until a measurement is made, after which the correlation is revealed.

A reasonable example is that of a pattern. A pattern represents collective information that isn't apparent unless the entire pattern is observed. That's a classical pattern! Such a pattern can be said to always exist, regardless of whether it's measured. For the quantum version, there may be two or more possible patterns, which all exist in an abstract space. However, just a single local measurement will select the entire pattern that will be observed. That means a local measurement seems to have a nonlocal effect. However, that nonlocal effect is not apparent at the local level. You need to see the entire pattern, which entails making lots of local measurements and comparing them.

Vector space does not mean vectors in space.

The first step is to visualize a vector field: — jgill

What's the purple line in your picture above? What's the green dot? A particle? Is it a trajectory (purple) of a particle (green) in a vector field? What do the vectors represent? What creates them? — Thunderballs

This is a relatively simple vector field in the complex plane based upon the function f(z)=-cos(z). The contour is a streamline describing the path of a point moving under the impetus of f(z). I suspect quantum fields are far more complicated and elaborate than this one. Kenosha Kid might chime in if he is around for an expert opinion.

Physical field theory seems quite different, involving tensors,etc.

Too much overlap. But false info can lead to false knowledge and then to false wisdom.

What if the asymptote doss not tend toward a numerical value, or even a mathematical principle, but to a re-characterization of all values? Calculus is a reduction to infinitesimal of values not definable mathematically. But it requires regarding those values (deviating from law) as "negligible". It also requires using them as a positive value for part of the rationalization of that neglect, but then as zero to complete it. — Gary M Washburn

This is a strange statement.

What is the math of the whole field of QFT describing? — Thunderballs

The first step is to visualize a vector field:

↪jgill
None of which shows that an eternal being exists necessarily. — Banno

Nothing to do with my passing comments on math singularities.

furthermore, if space itself is born out of some non-dimensional point, then what is the essence of that non-dimensional point? — TheGreatArcanum

Points of singularity, whether in the physical world or mathematics, allow bizarre behavior in their neighborhoods. I dabble in the complex plane where these things appear now and then. Even in that well-trod territory there are minor differences of definition. The most severe singular point is called an "essential singularity" and weird things happen in its vicinity. Most, if not all, such points connect to the function f(z) = exp(1/z), which takes on all complex values infinitely often in any neighborhood, no matter how small. Is there a counterpart in the physical universe?

The "shut up and calculate" remark, made by David Mermin, was meant to discourage people from . . . — TheMadFool

Like others, I attributed this wonderful line to Feynman. Mistakenly it would appear. Thanks.

I don't know why QFT doesn't get explored all that much on this forum. — PoeticUniverse

Oh oh. Awakening a slumbering giant! :gasp:

Busy day for the moderators.

I'm not chasing after anything with philosophy; I'm simply watching it flow past like a murky stream. The days of the classical philosophers are gone, but their dated thoughts come up over and over. That's fine with me. The natural sciences and mathematics have moved on and philosophy has given way to speculation leading to advancements.

However, philosophical discussions on social and legal issues seem relevant.

Core mathematics make up every single individual that; is, will, or in concept can manifest. — ExistenceofSelf

According to Max Tegmark all of reality is a mathematical construct. He's gone far beyond your limited view.

The question I have is: given how critical this moment is, what can be done to help it become reality? — Xtrix

So, this thread is not about discussing the bill, rather doing all one can to assure its passage. OK

:up:

Or do some still believe activism, politics, and topical issues are below the man of thinking, the intellectual? — Xtrix

Certainly not. I would be happy to vote for Joe Manchin for president should he be the democratic nominee in 2024. I seem to recall that Tocqueville made a comment to the effect that once a majority finds it can vote itself privilege and money democracy is in deep trouble. Of course his notions of democracy were varied. $3.5 trillion is excessive. Merely inflationary at best.

Bret, your website doesn't come up.