When one rich person leaves and one poor person moves in. It's happening. Not necessarily one-to-one. But in general.

A long time ago a good friend of mine, a young man at the time, inhabited a world that was falling apart - or so he perceived it. He had no job, despite an advanced degree in the sciences, his wife threatened to leave him and take their two small children. He was at wits end.

His wife, a devout Christian, insisted on him joining her father's church (her father was pastor), or she would leave. He gritted his teeth and joined the church - and focused on acquiring the "belief" upon which the church was founded. In other words, he told himself, "You will believe what they believe".

Some would say, You can't believe something you don't believe down deep - it will always be a superficial belief. But my friend would prove them wrong.

He not only came to strongly believe the faith, he became a missionary, working with prison inmates along the Gold Coast of Africa. He spoke with President Reagan about his work.

Now, here is the truly odd part of the story. His church was protestant, and my friend wrote published articles about the dangers of Catholicism. Then, one day, he and his wife and family converted to the Catholic faith, and he became a Deacon of the Church, working with the homeless.

If you make up your mind to believe, it's not an impossibility. And it's a possible way out of your dilemma.

If one looks at a kind of causation chain that has taken one from birth to the present, at each temporal step a host of causes converges to form the next step, not an easy thing to grasp. Stanislaw Lem had an Ergodic theory of history in which going back in time and performing an act wouldn't necessarily cause a radically different present. The fact that so many aspects of causation go into effect for a moment might mean that they "average out" and any one might have very little effect compared to the others.

The Grandfather paradox might not be completely binding. Give it some thought.

Trump appears to be in the mold of Mussolini - the arrogant stances and stern facial imagery. Back then the Italian people wanted someone to come in and bring order out of chaos, and he did, at least for awhile.

I wouldn't be giving Trump a second glance if it were not for the imbecile who is president now and the way he opened the borders of our country and allowed hundreds of thousands to migrate here non legally. I suspect the reasoning was to flood municipalities with people who would probably vote Democratic at whatever levels they could. Cities, counties, perhaps states. This might shift the House into Democratic hands. Non-civilians voting in national elections is problematic.

The irony is that the big Democratic sanctuary cities are losing high income tax payers to be replaced with homeless and welfare subjects.

Don't pay any attention to me. I'm old and doddering, the third stage of the Riddle of the Sphinx.

As a counterexample see my mathematical example. — jgill

Where?

But note that I specifically said that "an infinite sequence of events has no end". I didn't say that "an infinite series has no end". — Michael

Allow n to increase without bound (go to infinity) in the infinite composition (regression) ${{F}_{n}}(z)={{f}_{1}}\circ {{f}_{2}}\circ \cdots \circ {{f}_{n}}(z)$, which is an analogue of a cause/effect sequence. As n increases the value of this expression (the left hand end if you like) approaches a specific complex number.

And thus discovered/invented, together. What do you say, if you care to say? — tim wood

Creativity can enter when one speculates on new topics and definitions. If a flight of imagination leads to a new concept (if, in fact, there are any), then what flows from a logical analysis of this concept can be considered discovery. In other words, once the initiating concept is delineated, all that follows is in a sense immediately established - to be discovered. But the process of math research is almost always a sometimes convoluted combination.

Practicing mathematicians pay virtually no attention to this philosophical discussion.

The surprising effectiveness of mathematics in making accurate, sometimes unexpected predictions about the natural world suggests a deeper connection between mathematical structures and physical reality. This view opposes the idea that mathematics is just a tool invented for practical purposes, instead hinting at some intrinsic relationship between mathematical concepts and the fabric of the universe. — Wayfarer

Could be. :up:

I hesitate to enter this conversation, but I can't resist offering a few opinions held by an actual mathematician who has done both teaching and research.

The distinction between pure and applied math is somewhat vague, one reason being that pure math may become applied math at times. A researcher in applied math could be working on a math scheme to solve a particular problem, like calculating the stresses on a modern fighter plane during sharp turns. Or, he could be pursuing a topic purely for its own sake, curious about what comes next - and then finds someone has used his results in an applied manner.

This happened to me. My interests are always in "pure" math (complex analysis) and I published a paper in 1991, I think, with no thoughts of it ever being "useful", only to find my principle result was employed in a multiple author sociology paper about decision making in a group. Of course, the author who cited and used my result paid no attention to the details.

There are so many kinds of mathematicians and so many kinds of mathematics it's foolish to try to generalize. I'm guessing about 1200 PhDs are granted each year in the USA, with about half being American citizens. Probably a large majority never publish more than, say, two papers in their careers - for various reasons. But there are those, like myself, that find the exploration of new ideas fascinating.

That's how I see myself and many others: Explorers. It's no wonder you find mathematicians among rock climbers and mountaineers.

Pure math has connection to the natural world only as indecipherable signification representing thermodynamic equilibrium.
Since mathematicians only use pure math for investigation of the ground rules concerning applied math, pure math is merely higher-order applied math. — ucarr

Mysteries never cease :roll:

The point that I was trying to make is that if all had an equal chance of being selected individually, a smaller section of square is more likely to be selected then the larger scaled squares. — Philosophim

If we subdivide into 9 sub squares, the probability of choosing one of those sub squares is 1/9. If we have 25 sub squares, the probability of one of those is 1/25. Time to retire here, too.

If the past is infinite then the present is the end of an infinite sequence of events. An infinite sequence of events has no end. Therefore, the past is not infinite. — Michael

As a counterexample see my mathematical example. It has a front end but no past end.

Sorry. Language is a lot looser in philosophy (or this forum) than where I worked.

For every one square inch we see that has one chance out of the infinite, we have a square that subdivides down into magnitudes smaller, meaning in the comparative likelihood of one square inch, its much more likely that something appear very small. I don't want to math this out, maybe someone else could. — Philosophim

Take a one inch square. Divide each side into n equal parts. Then there are n^2 sub squares. Assume the probability of a point being in the big square is one, and each sub square probability then is n^-2. "One chance out of the infinite" means what? I have assumed the probability of finding a point in the big square to be one, but what you state implies zero probability. Thus there is really zero probability of finding a small object in any sub square.

They're called virtual particles — Philosophim

A mathematical convenience that cannot be observed through instruments.

Let think of an inch by inch square of space. Anything could appear in that square of space at any moment right? Right — Philosophim

Wrong. And I think you mean an inch cube in 3-space? Or an inch square in my favorite, the complex plane.

But divide the square in half. Anything could appear in that square at any moment, and not in the other half. Right? Right. — Philosophim

Wrong. Where do you come up with these flights of fancy?

What does this mean? For every one square inch we see that has one chance out of the infinite, we have a square that subdivides down into magnitudes smaller, meaning in the comparative likelihood of one square inch, its much more likely that something appear very small. I don't want to math this out, maybe someone else could. — Philosophim

Please don't. And don't ask a mathematician to do so. And something would appear very small if it is very small.

So over time its not surprising that we would see extremely small 'things' forming and unforming as they enter into existence, interact, and wink out — Philosophim

Since they can't be seen or observed, winking out is problematic. But there is a scale going from unobservable to observable, I believe. Where on this scale a virtual particle "becomes" "real" is interesting, though.

I love it when philosophers dabble in physics and math. Especially quantum physics. :cool:

I think in the long run, climate stories would be #1 — Mikie

Afraid Greta, Gore and many others have defeated their agenda with the American people by overzealous preaching and ridiculing. "Stupid people, wake up!! before you die of climate catastrophes"

But I'd move it up to #6.

I don't want to turn this thread into one regarding ontologies. — javra

Does a causation chain have being? It does if there is a dog at its end.

Assuming the Romney/Manchin ticket does not materialize. If it does, all bets are off.

I would vote for them.

Does an inch exist on a ruler without someone looking at it? — jgill

An inch no more exists without anyone contemplating it than does any word (such as the word “money”) exist without anyone contemplating it. — javra

I'm speaking of a ruler with inch markings sitting on the table in front of you. You turn away to ask your wife for a glass of wine, then turn back and look again at the ruler. Did it exist for that short period you glanced away? You know, Einstein and the moon.

Rabbit hole country.

A formatting question - sometimes I get a line feed before the math expression, other times, not - I don't see any obvious reason why. Any suggestion? — Banno

I use MathType, set to Wikipedia format, then change < to [ and > to ] at either end. It usually works but sometimes not, and I have no idea why.

The measures simply are. — jgill

That's a mistaken idea. Measurements need to be made, and measurement is an act which requires time. — Metaphysician Undercover

Does an inch exist on a ruler without someone looking at it?

the causal order A --> B --> C comes equipped with a dual order in the opposite direction, C --> B --> A. — sime

A-->B-->C-->A => C-->A-->B ?

It is really this phrase, "It simply is, there is no prior explanation for its being." that is ultimately true in any causal relationship. Do we call that a first cause? An uncaused cause? What do you think? — Philosophim

Mathematically, I would not. If an infinite composition exists it is the limit of a process that requires at each step a variable upon which that segment is defined.

${{F}_{n}}={{f}_{1}}\circ {{f}_{2}}\circ \cdots \circ {{f}_{n}}$ versus

${{F}_{n}}(z)={{f}_{1}}\circ {{f}_{2}}\circ \cdots \circ {{f}_{n}}(z)$

As n increases without bound one can look at the entire structure as a mathematical entity that has the value $\alpha =\underset{n\to \infty }{\mathop{\lim }}\,{{F}_{n}}(z),z\in S$

Now, outside the bounds of the theorem I have been discussing, alpha may not exist and the entire structure may oscillate or go to infinity, or whatever. Then the causation chain exists as a mathematical enterprise but cannot be associated with a particular value. It simply is. (My attempt at philosophy) :cool:

Pardon the intrusion into a less than delightful conversation. First, take the calculus out of the picture by considering ratios of distances, $\frac{\Delta y}{\Delta x}$. If the measure of y depends upon a measure of x, then for a small measure of the latter, like looking at the space of one inch on a ruler, there will be a small measure of the corresponding y. Time does not enter into the discussion. The measures simply are. One inch on the x-axis may correspond to two inches on the y-axis.

Now, if you throw in a quantum-like perspective ( a favorite tactic on this forum), the time it takes to look at each measurement counts. And you have complicated something very simple. Good show.

On the other hand to introduce time set $\frac{\Delta y}{\Delta x}=\frac{\Delta y/\Delta t}{\Delta x/\Delta t}$. Now we consider the passage of time in determining these distances.

An example might be the change in height of a hill with regard to distance from the peak. — Banno

The distance from the hill as one walks towards it grows smaller, and the line of sight distance to the peak also diminishes, but the height of the hill remains constant. The angle of line of sight grows also.

I mean, obviously, live people are more likely to succeed and reproduce than dead ones — Vera Mont

:lol:

Roughly? — Banno

Bull's eye, buddy :up: :cool:

The point is that if you take the entire set of the infinite regress and ask, "What caused it to be an infinite regress?" you realize that's the finite end. It simply is, there's no prior explanation for its being. — Philosophim

There are various ways to form analogues of causal chains in mathematics. One, that I initiated in a publication over thirty years ago concerns composition chains like

${{F}_{n}}(z)={{f}_{1}}\circ {{f}_{2}}\circ \cdots \circ {{f}_{n}}(z)$

In which one desires to formulate the individual functions to produce limits


$F(z)=\underset{n\to \infty }{\mathop{\lim }}\,{{F}_{n}}(z)$


A colleague of mine from the University of Tronheim discovered what is the most relaxed requirements to achieve this result, and went further to prove that as n grows larger and larger all values of z in a region of the complex plane will lead to the same result, that is to say $F(z)=\alpha$

Thus, we have a regression that at each stage begins with a specific z but ultimately all z's in a region give the same ultimate value. Looking at limits here.

"What caused it to be an infinite regress?": The design of the structure.

"you realize that's the finite end": No. That makes no sense, alpha is a limit, not a finite end. The further back one goes the more accurate the observed present day value of alpha. There is no finite end to this regression, only partial ends.

"It simply is, there's no prior explanation for its being" Yes.

If this thread continues I'll describe other analogues of infinite regression, for good or bad.

Various quantum effects, for a start — Banno

Probability and statistics can weave a tale as the story of quantum physics unfolds.

We know some things don't. — Banno

Huh. Please elucidate.

I own an Encyclopaedia of Philosophy (MacMillan) published in 1960s, and it is still very useful — Corvus

Yes, I can understand philosophy and history retaining their value over years. Science and math change much more.

The reasoning demonstrates that even an infinite regress falls into a finite regress of causality. — Philosophim

Why is that? I'm a little slow today. :chin:

Why do you believe so? — Corvus

They can't be continually updated, like Wikipedia. They cost $.

True, some knowledge doesn't change, but Wikipedia has that too.

As a captain in the reserves in the early 1960s, having done my obligation supporting ADC and SAC at a base near the Canadian border, I was asked to go active reserves (i.e., Vietnam) or resign my commission to make room for some other junior officer. I resigned my commission (being a math grad student at the time and married). But the USAF treated me very well while I was active.

How many degrees do you have, if I may ask? — frank

Three, plus post-grad certification for the USAF (and USWB) 1958-59 as a meteorologist.

It is easiest to simply imagine that all the [general] things known to humans that can be written down in language have already been written down. Now we have the {body of analytic knowledge}. — PL Olcott

So if listed, the listing might have to be refined as new knowledge is accrued. Still way to vague for me, but others may feel differently. I admire your tenacity on the subject.

A huge amount of progress has been made, but there are still problems, like the cloud problem — frank

In the late 1950s we had virtually no computer access when I was a post-grad meteorology student at the U of Chicago. (In 1962 at the U of Alabama there was a giant computer filling the wall, floor, and ceiling that was an ordeal to use.)

We learned to classify cloud formations. In atmospheric physics we studied droplets.

The body of all analytical knowledge — PL Olcott

Unless you can describe this vague notion as it might appear in a computer program - that is to say a list with #1, #2, . . . - I can't get beyond it to the conclusions you draw. @TonesInDeepFreeze is recognized as a go-to source on these kinds of subjects.

Will the textbooks and Encyclopaedia will still be in demand? — Corvus

The print textbooks will remain a primary source of specialized information. The print book encyclopaedia are dead ducks. Wikipedia is the best thing on the internet IMO.

Schmidt says climate models have come a long way from the simple energy balance and general circulation models of the 1960s and early ‘70s to today’s increasingly high-resolution and comprehensive general circulation models

Back then it was mostly statistical studies. Then after that period atmospheric physicists joined in and made it a real science.

The problem though, as I've read, is that this "moving apart" can be much faster than the speed of light. And since the motion of objects is limited by the speed of light in relativity theory, this "moving apart" cannot be categorized as motion, in order to avoid contradiction — Metaphysician Undercover

Yes. I stand corrected. The limits due to the speed of light seemed contradictory. It's difficult to imagine "nothing" expanding. It's an age of discovery and conjecture where our intuitions - formed by everyday experiences - must give way to a deeper reality in which math replaces direct sensations. And perhaps a newer, emerging math replaces that which has served so well up to this point.

Points and continuums, space and time . . . . . remain beyond complete understanding, although we manipulate them confidently. When I asked an old friend, an analytic number theorist, what he thinks of real analysis, he says, "It's very, very complicated and it starts with a metaphysical notion, points."

Years ago when George Bush was asked who his favorite philosopher was, he replied (after a bit of thought), Jesus Christ.

One can draw all sorts of conclusions from George's choice, negative or positive, but His teachings provide a way of life that could mitigate all those inequalities. Just a thought.

During the Pandemic the government (USA) gave out a lot of money, particularly to parents of small children. I remember thinking, I hope those parents don't use this for booze and drugs. I like to think that most didn't, but who knows?

The Meek shall inherit the Earth — jgill

what's left of it, once the Bold are done striving — Vera Mont

One of my old outdoor colleagues once said of my rock climbing,
He's not bold . . . but he doesn't need to be.

The meek are not necessarily the weak.

but denying that a trivial problem is a real problem, turns a trivial problem into something substantial — Metaphysician Undercover

Whether a thing is a problem or not is a societal decision. If the vast majority do not consider it a problem, it likely is not.

AI:

So, while Zeno's paradoxes, including the arrow paradox, are not considered unsolved problems in mathematics or physics, they do continue to inspire ongoing philosophical discussions¹³.

My understanding is that two objects move further apart with time; space itself (whatever it is) doesn't change. — jgill

However, I don't think it is proper to call this "motion" because the activity known as spatial expansion is not consistent with our conceptions of "motion", and the physical laws which describe "motion". — Metaphysician Undercover

From BingAI:

Yes, space does expand. The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time¹. This is an intrinsic expansion; the universe does not expand "into" anything and does not require space to exist "outside" it¹.
. . .
However, it's important to note that this is not a generally covariant description but rather only a choice of coordinates. It is equally valid to adopt a description in which space does not expand and objects simply move apart while under the influence of their mutual gravity¹. Although cosmic expansion is often framed as a consequence of general relativity, it is also predicted by Newtonian gravity¹.

Does "simply move apart" imply motion in the common sense? Can something move without motion?