How is an infinite line between 0 and 1 constructed? — Raymond

A Short Note: Extending the Diagonal Paradox

It's not a paradox — T Clark

:sad:

My feet don't follow the discontinuous path of the stair. — T Clark

The path is continuous. Sounds like you just float up. :gasp:

It's amazing how vast math is; the same goes for other disciplines too I suppose — Agent Smith

Over 24K physics articles on Wikipedia. :gasp:

So, on a purely logical basis, a "mathematical universe" makes no sense to me — Alkis Piskas

It's a stretch, isn't it? I think Tegmark's ideas somehow hinge upon the notion of "isomorphism" - the physical universe is the "same" as a purely mathematical structure up to an isomorphism. But I haven't really read his works.

Also, I think you’ve mentioned some mental health concerns before; struggles with happiness, etc. This should be a great opportunity to see what makes you happy — Pinprick

Buy a Boeing 707 and hire a crew on standby. Just a thought.

The New Age holds so much promise and this is such an exciting time. There is a chance of a new enlightenment that will be manifest in consciousness so different from the past, the people of the future will not be able to relate to the primitive lives we have had . . . — Athena

This is dialogue right out of the wonderful 1936 film Things to Come

I thought mathematicians were very keen to find some practical use for their theories. — Agent Smith

Most are not concerned about this, being immersed in their explorations of the subject. Staggering isn't it? Over 20K math topics on Wiki.

You're only the second billionaire I've spoken with in my life, incidentally. (That I'm aware of.) — Xtrix

Congratulations on your good fortune. My only experience with a billionaire was to drive around Jackson Hole sixty years ago in a model T with him picking up pieces of scrap metal from junk piles. He was a dirtbagger back then.

This eerily reminds me of Alexandre's paper. A breakthrough in perspective, this time not in physics but art and literature.

Is it like this all the time and everywhere? All sizzle, no steak!? — Agent Smith

Try this on for size: Catastrophe theory

I had a math friend, a fellow climber in fact, who worked with Thom. This topic made a stir when it first came out. Not so much now. I recently discovered there are 22,705 math articles on Wikipedia. Catastrophe theory ranks mid-importance and has a daily average of 4 views. My math page is low importance and has 16 views a day. Trivia.

The only thing left to do is to accept the wrath of the almighty Creator, succumb to His Divine Word, bow to His Infinite Creation, and show eternal gratitude for His Wisdom, given to us by His Word, to be heard by submissive prayer only. Let's pray He will get a grip and restore Natural order. If not, we are doomed for sure. — Raymond

Maybe you should skip Bible Study Group next week. Take a breather. :roll:

Conceptual reconstructionism in science? Mathematics?

Chaos theory is BS! :grin: — Agent Smith

Quite possibly. I prefer interesting quasi-symmetric patterns emerging from dynamical systems.

If we don't want birds to fall from the sky, seas to devour, superstorms to rage, sweet water to taste bitter, unworldly screaming to be heard from within, the last trees to burn, the dark to enter daylight, and the light to ruin the night, the pace must be lowered this very moment. It will be too late tomorrow. — Raymond

Truly Biblical! I'm speechless. :scream:

I am wondering how the discussion would go if we thought the Creator manifested our reality by giving chaos order and that human activity can either maintain that order or destroy it? — Athena

If you speak of chaotic systems, then chaotic theory searches for underlying patterns and deterministic formulae that depend upon initial conditions in a very sensitive manner, so that iteration leads to what is generally thought of as chaos. Are you saying the Creator made all chaos deterministic at the beginning of time?

To destroy that order would mean human activity could somehow alter these initial conditions, traveling back in time.

In general meteorology is far too complicated to involve such deterministic systems. Ecosystems lie on what is referred as the "edge of chaos".

I suspect you meant to trigger dialogue in a much less sophisticated scenario. Initial conditions being in play at the present time, such as global temperatures rising at a rate determined by conditions prevailing minus humankind, then humans messing that up with fossil fuels.

Perhaps it would clarify the arguments if placed in the following stark scenario: A scientist creates a robot that he programs to kill the first human it encounters. This happens and the robot is secured and returned to the laboratory, but the scientist is nowhere to be found. Other scientists confer, some wanting to dismantle (destroy) the robot, others wanting to attempt to reprogram the creature. The latter group prevails. So the computer brain of the robot is scrutinized closely to see if it can be altered and the critter returned to society in a manner in which it helps humans. Several scientists say, yes, it's possible, but another few say, no, we can't be sure - if there is the slightest chance it might revert to its previous condition we must not proceed.

It is finally agreed the robot is to be destroyed. :meh:

Lounge perhaps? :chin:

I think a distinction between my unconscious decisions and actions and conscious ones is artificial and pointless. — T Clark

Perhaps a conscious decision is one where we logically weigh all factors and do some sort of analytics to determine a course of action, whereas most decisions just seem to come to us after pondering. I see a difference.

I have my doubts about free will. Many decisions seem to pop into consciousness from hidden areas of the brain. However, we do have agency - the ability to act on these decisions. A potential criminal may have a strong desire to commit a crime due to circumstances affecting his mental state, but he has the agency to act or not act on that impulse. If the former, off to prison.

How is identifying as a Democrat equal to CNN being left? — Manuel

Ask the researchers at MIT, I suppose. Makes no difference to me.

Why is there not therefore a paradox? — hypericin

Probably because points have no dimension. The real numbers are complicated and fascinating.

Look, suppose I pick at random a point in the interior of the cube: (.251956... , .629435..., .194735...) Then that point corresponds to a unique point on the x-axis edge: .261529194947...

You just alternate digits. Here, you do it by going the other way: find the point inside the cube corresponding to the point on the x-axis: .381402258639...

The process is continuous in the epsilon-delta sense.

https://web.media.mit.edu:

Just like the American average, our survey and the published surveys we studied show the
majority of CNN’s audience identifies itself as Democratic. The largely leftist audience has
probably had a significant influence on CNN’s reputation as being a left- leaning news
organization.

Yep. It's an algorithm for you to guess demonstrated by the example. Standard stuff. :cool:

Then there's that hypothetical spaceship we are in, approaching a Black Hole at a constant speed. We sail in and if not annihilated continue our explorations. But a friend is watching our progress from a great distance and sees us going slower and slower until it appears we have stopped before penetrating the anomaly. To him, we will sit there for eternity, gradually inching towards the periphery - like a mathematical limiting process, never quite making it.

(I'm not a physicist, but I recall reading of this. Could be wrong)

However, these companies are beginning to lose many of their viewers. It appears that audiences are tiring of combative and demeaning dialogue. — jgill

I think it's just polarization. Fox viewers aren't getting tired of Fox and CNN viewers aren't getting tired of CNN. But Fox gets few CNN viewers and CNN gets few Fox viewers. It's a tradeoff between loyalty and reach. — SophistiCat

From Forbes (1 Dec 2021):

Overall, the cable news networks saw ratings drop significantly from the same month one year ago, as the coronavirus pandemic coincided with the presidential election, driving heavy viewership. CNN experienced the most dramatic decline, dropping 77 percent from one year ago in prime, followed by MSNBC (down 59 percent) and Fox News (down 35 percent). The drop-offs were even bigger in the key demo, with CNN experiencing a year-over-year decline of fully 84 percent in prime time. MSNBC’s decline was 74 percent, and Fox News had the smallest year-over-year drop, down 49 percent.

The news media gives its viewers what they seem to want. CNN tilts to the left and FOX tilts to the right in their presentations (evening news, e.g., not their numerous and sometimes rabid commentators' shows). However, these companies are beginning to lose many of their viewers. It appears that audiences are tiring of combative and demeaning dialogue. ABC, NBC, and CBS don't seem to be caught up in this audience decline.

The fact that the line, plane or volume have the same cardinality is because of the attempt to reduce them to points — AgentTangarine

Ignoring the references to cardinality and accepted theory , it does seem like the unit cube has more of "something" than one of its edges.

The bijection between R and RxR is not continuous — AgentTangarine

Really?

This is the same crank whose banning you were lamenting earlier because (he says) he is a physicist and we should be grateful for him being here to educate us... Be wary of unhinged bullshitters confidently throwing around specialist terminology. — SophistiCat

I'm well aware of the situation. :cool: Having communicated with him I believe he has a graduate degree in physics. However, his concerns are with the "physical" or interpretive aspects of the science rather than mathematical descriptions. Even advanced math in QT seems not to have reached axiomatic set theory to a noticeable extent. Kenosha Kid is another genuine physicist. To the best of my knowledge neither of these gentlemen work in the profession at present.

Sounds good mr. Gill. Almost convincing. But you construct a new number from the both. Giving them both different decimal places. The diagonal proof of Cantor says you leave numbers out. Infinitely many. — AgentTangarine

Give me an example of a number you think is left out. I bet it's not. Avoid the .999... =1.0 thing. Have you figured out what the algorithm is?

Too, the definitions in math give me the impression that true understanding is being sacrificed for logical formalism. — Agent Smith

The definition you are seeing is the formal aspect. It's a kind of final touch to an idea that began as an interesting notion.

Take the square {(x,y):0<x<1,0<y<1} and map it one-to-one to the line {r:0<r<1) by using the procedure implied by the simple example (.329576914..., .925318623...) <-> .39229537168961243...

You can figure it out if you stay off the Xmas grog long enough. Although you are a smart physicist and may be pulling our legs. You and Agent Smith can work this out. It cropped up in the course I used to teach in Intro to Real Analysis.

Hence, there are exactly the same "number" of points in the (section of) the plane and on the unit interval. Same cardinality.

This is the correspondence between infinite and infxinfxinf. And if r goes to 0.04566..., or 0.005667... or 0.000556654... (you get my point, I guess...) even infinite times are included. So the map becomes one between inf^2 and inf^4. Aleph1 and aleph2 — AgentTangarine

Are you off your meds again?

You guys need to get a hotel room. — jgill

Disgusting. — TonesInDeepFreeze

Pardon me, Ma'am. Here in the bunkhouse on the prairie I tend to forget there are ladies present. :worry:

I jumped up a dimension to make a point. R^n has the same cardinality as R.

You guys need to get a hotel room.

Repeat for page 2:

That would imply that the covered piece has the same cardinality as the whole square. — AgentTangarine

This is getting painful to watch. A simple example shows that the "number" of points in the interior of a cube {p=(x,y,z):0<x<1,0<y<1,0<z<1} , is exactly the "number" of points on the line {r:0<r<1}:

1:1 correspondence demonstrated by r=.3917249105... <-> p=(.3795..., .921..., .140...)

Extending these ideas shows the cardinality of R^3 is the same as that of R. — jgill

Computers play music.

That would imply that the covered piece has the same cardinality as the whole square. — AgentTangarine

This is getting painful to watch. A simple example shows that the "number" of points in the interior of a cube {p=(x,y,z):0<x<1,0<y<1,0<z<1} , is exactly the "number" of points on the line {r:0<r<1}:

1:1 correspondence demonstrated by r=.3917249105... <-> p=(.3795..., .921..., .140...)

Extending these ideas shows the cardinality of R^3 is the same as that of R.

Ha! You think there is a connection? :) From my own experience, I've known a few physicist and astronomer climbers, but can't recall any mathematicians off the top of my head — SophistiCat

Yes, I do think there is a connection. I knew and climbed with ten or so fellow math guys from different locales over the years. For me it was problem solving and exploration. Short rock climbs are frequently referred to as "problems". A great combination of intellect and athletics.

If you’re looking for living fossils, I’d start with the Republicans. — Joshs

But they're not likely to fund your fossil mind project. The Democrats will print up a dumpster full of money for you. :cool:

Nowadays we also invent a load of completely useless mathematics, of which perhaps a small fraction will ever find an application, and the rest will gather dust in mathematical journals and specialist books. — SophistiCat

I agree. Many years ago I was on a USAF Office of Scientific Research grant. At the time I was grateful for the financial support, but I wondered why they would fund the sort of things that interested me.

I mentioned 135 math research papers a day received at ArXiv.org . Today it was 269.

What motivates all those math people? Tenure/promotion considerations. Prestige within a community. Delight in the exploratory aspects of a subject with few constraints arising from the physical world - free rein for one's imagination.

From my vantage point as a very senior citizen, the first thing I note is the huge number of people pursuing activities compared with 60 years ago. I haven't a clue as to numbers of mathematicians then and now. But at that time the outdoor sport I became involved with had perhaps a couple of thousand fairly serious devotees here in the USA. Now there are well over six million. World-wide there may be ten million or more. It staggers the mind.

Let's be careful we don't consider the following and similar scientific studies racist. There are differences related to origins that should not be fodder for racist rants:

Ethnic Anatomical Differences . . .

Sickle Cell Disease . . .

Interesting article if a bit long-winded. Two nit-picking comments:

1.

Well, the history of science has proved that whatever complex concepts mathematicians created, they finally came to be applicable in the mathematics of physics or even to directly describe an empirical context.

The massive amount of "pure" mathematical knowledge produced in the last three hundred years suggests this statement is unsupportable.

2.

In 1950, Nicholas Bourbaki, who shaped the concept of mathematical structure and types of structures from a set-theoretic perpective, asked in his influential The Architecture of Mathematics whether the unity of mathematics is the outcome of formal logic or simply this scientific fertility.

It would appear from this statement that "Nicholas Bourbaki" is an actual individual, when in fact it's a name a group of math people created when pooling their resources and producing a number of respected textbooks.

Nevertheless, an entertaining read. Thanks.

My 'anti-platonist pragmatics' (finitism?) comes to this: pure mathematics is invented (re: pattern-making) and applied mathematics is discovered (re: pattern-tracking) — 180 Proof

Pure math stems from explorations in applications frequently, though not exclusively. The stuff I have done for years was pure up front and has remained so. It's a combination of discovery and invention.

From Wiki:

In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics.

Can you tell me what is meant by "the complex plane"? — Metaphysician Undercover

Complex Plane

The issue is that a whole never really is a symmetry, so that is a misrepresentation — Metaphysician Undercover

I tend to think this too. But I'm tolerant of math and physics.

Like I said I've had experiences that make the "real world" feel like a joke where everything felt more real then "reality". . . — MAYAEL

It was about forty-five years ago when I decided to try Castaneda's simple instructions. They worked the first time, and the experience was astounding. No drugs. To become pure unrestrained will is indescribable. However, picking up a newspaper in this realm I could see the print clearly but could not process the meanings of the words.

We see what we consider physical reality and our minds process what we see or otherwise experience. When the processing is separated from its input the mind becomes very creative. More philosophers should engage rather than only talk. Just my opinion.

AgentTangarine is a bot. Not a real member posting. Can we put a restraining feature on this bot? — Caldwell

Then what? Return to quantum babble? Be thankful there are a couple of physicists on board. :roll: