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

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.

You haven't proven any math. But you have proven yourself to be a crank. — TonesInDeepFreeze

Then prove me wrong!

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}: — jgill

N can be mapped infinite times onto [0-1]. It can be mapped infinite times on a vertical linepiece. So infinite times infinite times on the square.

In an any case, you show no evidence of genius. Very much to the contrary. — TonesInDeepFreeze

I have no intention to be one. But that's what they say. Like being crackpots.

I gave you the primary formulas that you need to start with. You ignore them then complain that I haven't given you any math — TonesInDeepFreeze

Which functions? Of repeated fractions?

She certainly can-can." - Cole Porter — TonesInDeepFreeze

And anything goes!

And that directly contradicts your claim now that we can map N onto R one-to-one. — TonesInDeepFreeze

We can! An infinite times infinite times actually. One time onto 0.1-0.9999999. This can be done an infinite times for [0-1]. And an infinite times for the whole real line. Hence aleph1.4, and not aleph1.

There wasn't much to 'see' in the Big Bang, because for the first 240,000 - 300,000 years, there was no light. Don't know about other radiation in the spectrum. Anyone? — Bitter Crank

You could look at neutrinos. Offers you a glimpse how it was a fraction of a second after the bang. But I can already tell you that looks the same as the CMBR. I advocate for a new mission! Let's shoot a 1000000 billion cube water basin into orbit! To observe neutrino distribution away from the Sun. Must give a spectacular view. A NBR view on the 10exp-35 seconds ATB! Oeoeff!

Maybe replace "see the world" with "light sensitivity.". — frank

Light sensitivity is a function of the eyes. Seeing is a function of consciousness. You need it to see worms. To see the world. But you can exclude the worm or the world. Focus on consciousness alone.

Delusional and disconnected from reality. Check for fever. — TonesInDeepFreeze

That's what is said about geniuses in general. Like being a crackpot. Untill now I haven't seen one bit of math, only parrot references to the net. The cardinality of RxR being the same as R. I gave you a link to a so-called proof of a bijection between R and RxR. A wrong one. I asked you why it's wrong. No reply. Cantor didn't take the infinity of the real line into account in determining how many powers of an infinity are needed. You only replied that you can't raise infinity to a power. You just need inf^3 times to enumerate all points on a line. Saying that the aleph of a 2d infinite plane is the same as that of an infinite line is the same as saying R is the same as N.

Who is FZ? And why does it matter that he lived 120 years ago? — TonesInDeepFreeze

Fraenkel and Zermelo. Old-fashioned. They, like Cantor, overlook one infinity.

Whatever, dude. — Paine

Yeah, whatever... Keep up your spirit of awe! Oooohh, pictures!

f it is only something that cannot be demonstrated to others — Paine

Webb can only show pictures. Now that makes you understand! Webb can't look at the big bang. I can. Like all people with imagination.

If it is only something that cannot be demonstrated to others, then only silence will suffice. — Paine

What on Earth are you talking about? Why should I stay silent? Because it's a silly project?

That must be really cool for you but useless for your brothers and sisters. — Paine

You think your brothers and sisters are interested in photographs of a 100 million year old galaxy? Nothing to be learned from that.

That must be really cool for you but useless for your brothers and sisters. — Paine

My brothers and sisters? My sister is not one bit interested. Like most people. Except a few "chosen" ones.

The notion that you have information is suspect as such. — Paine

Why is that suspect?

We live in the bit of experience life offers to us.
The notion that you have information is suspect as such. Who made you the wizard of worlds not available to us ordinary humans? — Paine

The wizard of worlds? I didn't create it! But I do understand it. With or without Webb.

I have offered the most actual info of all...It's a waste of money. Pure thought brings you a lot further. For free. No Webb needed.

What are those? — The Opposite

"Hubble Space Telescope. In astronomy: Dark energy …1980s astronomers began to use Type Ia supernovae as standard candles"

They are standards of light intensities. They all are about the same. It was discovered that some of them stand further as expected. Which implied accelerated expansion.

The opportunity to get data about the early universe is seriously important. — Paine

Are you serious? It's already obvious to me what happened at the big bang and before (which can be better described as far away from us).

Yes, they work so long as we don't mask (and socially isolate) our healthy vaccinated population. — Roger Gregoire

What has masking to do with working? It works also when masking. Are you saying it works only if you don't mask because healthy people take away viruses around the fragile people?

That was it. Thanks for your contribution. The idiots have set the zeitgeist, since at least the time of Thatcher and Raygun. Perhaps, one hopes, their time is done. If not, we all might be done. — Banno

We're all done. As individual people are these days, there hasn't been more conformity ever before.

But if a functionalist says consciousness is identical to function, but excludes worms, they'd need to explain why. — frank

If you exclude worms from the function of consciousness to see the world, what's to be explained. Note that the function of consciousness (to see the world) is not the same as explaining it. You need consciousness to walk around. But that's no explanation.

a piece of music is nothing but a pattern. you just call it music since it alleviates your boredom and raises your dopamine — Miller

That's not why I listen to music. That's how you see it. A sad, almost terrifying fact. The soundwave pattern of music cannot be thrown in a mathematical formula. Only short pulses of music can. So what use has math? Not to mention the feeling you get when listening. Just a pattern on the neural network resonating with the music waves. But it feels great! How you explain that?

True enlightenment is realizing that all we have are stories about reality. After years of living in the dark (though light for the ones living the story!) of a supposed true reality, this realization opens your eyes and makes you bath in the bright and warm light it shines out. It's a kind of enlightenment that sets free and makes you appreciate other stories.

Anyway, you said you were off, Eliza. Too bad you didn't mean it. — TonesInDeepFreeze

Why? It's not as boring as I thought. There are even alephs0.5 and alephs0.99 or alephs0.01. If there are alephs(sqrt2) remains to be seen. A closed interval on the real line, like [0-1] can be fit infinite times on the real line, so in fact the cardinality of the real line is 1.4. That of the 2d plane is about 2.6. That of the 3d volume is about 3.2. That of a fractal line, plane, or volume, lies between these. Cantor didn't realize this yet.

Coming to think about it, of course aleph(sqrt2) exists. And the aleph for [0-1] is in fact aleph1. Cantor overlooked one infinity! Which only shows his genius! Who can overlook infinity...?

It's gotta be understood though that the cover of a square by a fractal curve is not the same as just cutting out that part of the continuous square. That would imply that the covered piece has the same cardinality as the whole square. The fractal line doesn't cover the whole part. Like a fractal collection of points doesn't cover a continuous part of an interval (it can be piecewise continuous though.).

As if you are a mathematician... Keep it up Cantor! Why I write inf^1 is to highlighten the concept of cardinality. FZ lived 120 years ago. The axiom of choice is based on finite sets. Inf^3 might sound nonstandard in your ears but it's just infxinfxinf. What's so difficult about that? You have to raise 2 to the power 1.6 or something to obtain 3. So the aleph is aleph1.6, approximately. The fractal line occupying part of the square has aleph1,6 multiplied by a factor to account for the degree of covering.

The claim that aleph_1 = 2^N is the continuum hypothesis. — TonesInDeepFreeze

Then you have a different notion of aleph one. The ordinal in Aleph one is just related to how many times the infinity is present. For the naturals inf^1, so aleph 0. For the line inf^2, so aleph1.. For the 2d plane inf^4, so aleph2. For a volume inf^8, so aleph3. For a 1d fractal, say inf^3. So aleph1.6, approximately.

I just mean inf x inf.

I have not mentioned continuousness. I have merely pointed out the utterly well known fact that it is a theorem that card(R) = card(RxR),. — TonesInDeepFreeze

Yeah, you have said that infinite times already. It's just not true. There are inf^2 points between 0 and 1. Aleph1. There are inf^4 of them in 2d. Aleph2. In 3d there are inf^8. Aleph3. I'm off. It's boring.

Well, it's not. Between aleph1 and aleph2 lies aleph1.5. A fractal line occupying half the square. There are inf^3 points for this figure.

- There are very few (or no) syntactic mistakes.
- The ideas are clear and well-written.
- It says something philosophically interesting.
- There are no logical fallacies.
- There is no plagiarism.
- The paper is on-topic.
- Forget about word counts, fonts, APA format, and all other 'peripheral' issues. — jasonm

Only the second point is truly important. Maybe the fourth too, but that needs no mention. Say something interesting or new and you got a B is in the pocket.

So, JWT (or JWST) can tell us about the early evolution of galaxies, but she didn't explain what we would specifically find out about dark matter/energy. — The Opposite

Maybe a bit about dark matter, if you could find rotation curves of the early galaxies. You could find something about the receding velocity. And find that it was less than the recession velocity of closer galaxies. By means of galactic candles. But nothing essential.

Vaccinations work. In the short term for sure. It's the question if it works on the long term. Many antibiotics don't function anymore. What if the virus again mutates? New boosters? How does this work out on natural immunity? Will it get immune to vaccination, which means it says: "Let the virus in! No real thread to be expected, as last time we didn't get sick, so why bother now?" Stimulating it periodically with stuff that's innocent will possibly render it useless after a few times.

before you were born you were nothing but a strand of dna — Miller

I was nothing but the stuff around it. I just used my genes to develop. They only gave me proteins. They were not involved in any programming. My brain can act like a computer but it isn't one. The physical world can resonate in the brain. This resonance can be structured by math. But only for certain well defined experiments to fit the math. Most of the physical world can't even be approximated by math. There is no math formula corresponding to a piece of music. Any attempt to fit all phenomena in math is doomed.

Then you have to reread your proofs. Are you seriously implying that the cardinality of the 2-d continuous plane is the same as that of the continuous line? The cardinality of R is the power set of N. The cardinality of RxR is 2. There are obviously more elements in RxR than in R. That's why the cardinality of RxR is 2, of R it's one, and of N it's zero.

There could be cardinalities between 1 and 2. The fractals, with fractal dimension.

The points on the side of a square have c=1. The square has c=2, while a fractal curve in it has c between 1 and 2.

We can have as many bullets/mosquitos/viral particles as we want. The math does not change. I only used the 1 mosquito (or 1 bullet) to make the math (in calculating Risk Assessment) super simple for everyone to plainly see. — Roger Gregoire

Yes. But viruses belong to another class of stochastic variables. A virus doesn't fly around the room like a mosquito. The naked man doesn’t act like a lightning rod for the viruses, as for the mosquito. The mosquito might temporarily be occupied with the man's ass, as a load of mosquitos might. The same holds for a huge number of viruses entering the man. Inside the man they can't harm the woman. Mosquitos are search-and-suckers. Viruses only suckers The man might take some away, but later on he will emit new ones (despite of being immune), increasing the risk for the woman. They might even be introduced by him in the first place, which is what actually happened a few years ago. Introducing the naked man will indeed take viruses away from the room. But a lot will remain, and I doubt that paying the Chippendales for visiting the elderly centers is a good way to get rid of viruses in the rooms of faint-hearted ladies of 90 years old.

How do I map this onto how the words "opposite" and "negation" are used in discourse, formal and informal, outside math that is? — Agent Smith

An opposite number can be obtained by inverting it. You oppose the change, to let the situation stay the same. Multiplication by 2 can be opposed by multiplication by 1/2.
Negation on the other hand, means you don't want to change at all. When someone adds 7, you negate this by substracting 7.

So,

Opposition: multiplication by the inverse
Negation: adding the negative

The first opposes the change, after it has taken place, while the latter negates the change before it has even started, making it impossible to oppose at all. Tyrans are negators in the first place, while opposers in the second. The oppressed though hold opposition up higher then negation. They regard opposition as the most important, while negating the tyran.

You put the burden of proof on me. You contend though that a scientific approach is more reliable. Why? Because it offers a view on how it really is? That's circular.