Which science communicator do you find to maintain the most accuracy?

  • #1
syfry
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TL;DR Summary
Who do you rate as the most accurate in communicating science, in particular physics?
Was watching a Sean Carroll video and his answers to some questions seemed to run counter to the norm.

For example at 1:15:30 in the video, he seems to be saying that we'd see only a (hypothetical?) 'test particle' get stuck at the event horizon of a black hole.

Also at 1:17:19 in the video, he claims that Einstein wouldn't have added in the cosmological constant into general relativity if he had known the universe is expanding, implying that wouldn't have been necessary to add in. Which sounds strange because that addition seems so crucial to everything about vacuum energy and whatnot.

Hopefully while replying you won't be concerned about Sean Carroll seeing your reply if you contradict his claim. 😄

Anyway, inaccuracy adds big hurdles to understanding physics, at least in my case. So a list of the most accurate science communicators would be helpful.

For the record, I still perceive of Sean Carroll as being highly accurate in most of the video, but that's a feeling based off of my limited knowledge. Surely, you know better than I do about his level of accuracy.

I'm asking specifically about the accuracy of science communicators. Who do you rate as most accurate?
 
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  • #2
syfry said:
Who do you rate as the most accurate in communicating science, in particular physics?
Given that Sean Carroll is not a particle physicist, clearly somebody else.
 
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  • #3
syfry said:
Was watching a Sean Carroll video and his answers to some questions seemed to run counter to the norm.
Not really. See below.

syfry said:
For example at 1:15:30 in the video, he seems to be saying that we'd see only a (hypothetical?) 'test particle' get stuck at the event horizon of a black hole.
Yes, and he's correct. A "test particle" by definition has zero (or at least negligible) mass and therefore adds zero (or at least negligible) mass to the black hole. And therefore the hole can be considered stationary while the particle falls in, and we can use the standard Schwarzschild geometry to predict what happens and what we see, which is what Carroll describes at the point you refer to.

But if an object falls in that is not a test particle--i.e., which will add non-negligible mass to the hole when it falls in--then the hole is no longer stationary and the standard Schwarzschild geometry can no longer be used to predict what happens and what we will see. You have to do a more complicated analysis. Carroll explains exactly this a little further on in the video.

syfry said:
Also at 1:17:19 in the video, he claims that Einstein wouldn't have added in the cosmological constant into general relativity if he had known the universe is expanding
Yes, and that is correct if we take Einstein at his word when he said, after the expansion of the universe was discovered, that adding the cosmological constant in order to make his static universe solution possible was "the greatest blunder of my life".

syfry said:
implying that wouldn't have been necessary to add in.
Which, at the time, was true; there was no evidence whatsoever for a nonzero cosmological constant.

syfry said:
Which sounds strange because that addition seems so crucial to everything about vacuum energy and whatnot.
Which (the accelerating expansion of the universe, which requires a small positive cosmological constant) was only discovered in the 1990s, many decades after Einstein made the statement I described above.

So I dispute your claim that what Carroll was saying was inaccurate.
 
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  • #4
Vanadium 50 said:
Given that Sean Carroll is not a particle physicist, clearly somebody else.
I'm not sure whether the OP meant "particular physics" as "particle physics". The items he points out in Carroll's video are analyzed using GR, not particle physics.
 
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  • #5
syfry said:
I'm asking specifically about the accuracy of science communicators. Who do you rate as most accurate?
I think this is squaring the circle. You cannot speak to a broad public audience and require explanations at the university level. It is a bit like comparing (what do you use in English?) apples and oranges?, apart from the fact that "most accurate" is highly subjective.

I once went to the university (as a high school kid) and made my way to a particle physicist. I was only searching for information and basically for the answer to what I should read. (It was the pre-internet era.) The professor handed me a journal with plenty of data on actual experiments. I think it was mainly a collection of protocols at some collider. I was really proud of my prey, however, I didn't understand a word.

My personal opinion on "science communication" is
https://www.physicsforums.com/insights/opinion-when-pro-scientists-explain-using-pop-science/
 
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  • #6
PeterDonis said:
But if an object falls in that is not a test particle--i.e., which will add non-negligible mass to the hole when it falls in--then the hole is no longer stationary and the standard Schwarzschild geometry can no longer be used to predict what happens and what we will see.
Emphasis mine.

I'm having trouble understanding something.

He did explain less than a minute later, that "in the real world", the "event horizon expands a little bit, to swallow them up; so what we see at the end of the day, is not things that are infinitely redshifted and moving infinitely slowly, they move slower and slower and slower and then bloop they are in fact swallowed up by the black hole." (emphasis mine and quotes are his words precisely)

Sounds predictive enough. That's where I'm having trouble in understanding since his point seems to run counter to the norm.

If he meant something else, why did he word it that way?

Which (the accelerating expansion of the universe, which requires a small positive cosmological constant) was only discovered in the 1990s, many decades after Einstein made the statement I described above.
Emphasis mine.

Having trouble understanding here as well.

I'm assuming general relativity had gotten along fine for 75 years without that discovery in 1990s. If so, sounds like the cosmological constant is able to be entirely standalone.

In other words, if Einstein had chosen differently and instead someone else had later modeled a standalone cosmological constant (in a similar style of the Hubble constant), then it might've stood on its own as a known fact and the equation for general relativity would merely be slightly shorter in length.
 
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  • #7
PeterDonis said:
I'm not sure whether the OP meant "particular physics" as "particle physics". The items he points out in Carroll's video are analyzed using GR, not particle physics.
Correct! I could've as well said, "particularly, physics". If 'particular physics' is another way to say particle physics, I wasn't aware. Thanks.

If the word particular is
 
  • #8
fresh_42 said:
I think this is squaring the circle. You cannot speak to a broad public audience and require explanations at the university level. I
To paraphrase Anton Chekhov, or possibly Pavel Chekhov, or maybe someone else entirely, "A popularization is like a mistress. If it is beautiful, it is not faithful, and if it is faithful it is not beautiful."
 
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  • #9
fresh_42 said:
You cannot speak to a broad public audience and require explanations at the university level.
Even at the university level, explanations need to be tailored to the audience's level of knowledge. Kip Thorne, in his book Black Holes and Time Warps, recounts the story of Oppenheimer's first lecture as a professor at Caltech. It was a brilliant, highly knowledgeable lecture, but afterwards Richard Tolman, who had sat in, told Oppenheimer, "Robert, that was beautiful but I didn't understand a damned word."
 
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  • #10
syfry said:
Sounds predictive enough. That's where I'm having trouble in understanding since his point seems to run counter to the norm.
He's saying you can't use the Schwarzschild solution - a particular idealised case - to analyse this. You have to go beyond. Which adds complexity. He's not saying it can't be done.
Or, rather, you can use it, but you have to be mindful of how the underlying assumptions that you used to arrive at the idealisation can give you wrong predictions when you push into a regime where those assumptions can no longer be justified. It's the same for all physics.
Rather than committing the sin of overly simplified popularisation, Carroll shows here how overly simplified popularisations may lead you to arrive at an unphysical conclusion.

syfry said:
Having trouble understanding here as well.
The point is that Einstein couldn't have known which parameters have what values, before they were measured. There are many models of the universe that can be derived from his equations. By tweaking the free parameters you can construct scenarios that have the universe be steady, expand or contract, in an accelerated or decelerated (or a combination of those) fashion. That you, today, have heard about the accelerated expansion doesn't help anyone contemporary with Einstein. They had to go by with what they saw.
At first there was no evidence for expansion - so it was sensible to (provisionally - as always in science) exclude models that aren't static. Then there was no evidence for accelerated expansion, hence models with the cosmological constant were excluded from the subset of the non-static ones.
Now there's evidence for accelerated expansion - so the parameter that governs it has to be included in the model to fit the data.As to the question in the topic - of all the current physics popularisers I've seen so far, I actually find Sean Carroll to be the best. He's very careful not to overstep the limitations of his descriptions, pointing out where they fail, and has a knack for talking in an enlightening manner. I'd put him together with Feynman in the same A+ camp here.
 
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  • #11
PeterDonis said:
Even at the university level, explanations need to be tailored to the audience's level of knowledge. Kip Thorne, in his book Black Holes and Time Warps, recounts the story of Oppenheimer's first lecture as a professor at Caltech. It was a brilliant, highly knowledgeable lecture, but afterwards Richard Tolman, who had sat in, told Oppenheimer, "Robert, that was beautiful but I didn't understand a damned word."
And then there is the species of science journalists!
 
  • #12
syfry said:
He did explain less than a minute later, that "in the real world", the "event horizon expands a little bit, to swallow them up; so what we see at the end of the day, is not things that are infinitely redshifted and moving infinitely slowly, they move slower and slower and slower and then bloop they are in fact swallowed up by the black hole."
Yes, that is the outcome of the more complicated analysis I referred to.

syfry said:
That's where I'm having trouble in understanding since his point seems to run counter to the norm.
No, it doesn't. It's just a point that the "norm", as you call it, doesn't usually discuss at all. The "norm" is to only discuss the case of a test particle, often without clarifying that what you are saying is only applicable to that case--but nevertheless, the description for that case is still an idealization and the real world will never match it exactly.

One other point is also often left out that Carroll does not mention: in the real world, we can only detect a finite range of wavelengths of light, and once light from the infalling object is redshifted to longer wavelengths than the longest we can detect, we will no longer see it: it will appear to us to have vanished. In real cases, this will happen while the object is still a fair bit above the horizon.

syfry said:
If he meant something else, why did he word it that way?
He meant exactly what he said. See above.

syfry said:
I'm assuming general relativity had gotten along fine for 75 years without that discovery in 1990s.
The issue isn't "general relativity" as such. The issue is our best current model of the universe. Before the discovery of accelerated expansion in the 1990s, our best current model of the universe was compatible with the cosmological constant being zero. But after that discovery, it wasn't. So cosmologists updated their model.

As far as "general relativity" is concerned, the presence of the cosmological constant in the equations is perfectly consistent with GR and how it was derived. AFAIK this was known around the time Einstein proposed his static universe model, based on an exchange he had with de Sitter about the cosmological constant.

In fact, the main issue we see today with the cosmological constant is not why it is there at all, but why it is so small. A "naive" derivation of an effective cosmological constant from quantum field theory gives a value about 120 orders of magnitude larger than the value we actually observe. But to the extent that's an issue, it's an issue with quantum field theory, not GR. GR makes no particular prediction about the value of the cosmological constant; it just says that solutions with a nonzero cosmological constant are perfectly consistent with the field equation.

syfry said:
if Einstein had chosen differently and instead someone else had later modeled a standalone cosmological constant (in a similar style of the Hubble constant), then it might've stood on its own as a known fact and the equation for general relativity would merely be slightly shorter in length.
No, this is not correct. The cosmological constant is a term in the Einstein Field Equation of GR. It's not something that is "standalone". Nor is the Hubble constant, btw: the Hubble constant (which is not actually constant, it changes with time--except, ironically, in the idealized de Sitter solution in which the cosmological constant is the only stress-energy present) is a term in the Friedmann Equations, which are what the Einstein Field Equations reduce to under the assumptions of homogeneity and isotropy of the universe.
 
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  • #13
fresh_42 said:
I think this is squaring the circle.

A good place to start.

My personal approach with any such conundrum is to consider how we've gone about things, to examine what we've concluded by now, and then to ask: would've it always played out that way if the earliest step had veered a bit?

We cannot travel back in time to test that, so I instead muse about if that played out on hypothetical parallel Earths: what if, while people in ancient times on another Earth were refining a value for pi, someone had made a wire thin band, a 2 × 2 square, that with a stream of enough water pressure would snap into a perfectly circular shape? Now they might know the area of that circle is precisely: 4. No rounding and no infinitely dwindling values.

Maybe they continued to extrapolate the wire thin material with cubes that snap into perfect spheres.

It's limited, only works with squares and cubes, although they probably extend the possibilities by getting creative, but maybe the act of teaching the possibility with a real example of perfect squaring then opens up more avenues of exploration.

"Ok student, here's how we figured out this circle has a perfectly precise area of 4, and, here's how we calculate a really close approximation using pi. Now, how do we get from here to here purely by calculating on parchment? What math do we need to invent?"
I once went to the university (as a high school kid) and made my way to a particle physicist. I was only searching for information and basically for the answer to what I should read. (It was the pre-internet era.) The professor handed me a journal with plenty of data on actual experiments. I think it was mainly a collection of protocols at some collider. I was really proud of my prey, however, I didn't understand a word.

My hypothesis is that when we can easily lose our livelihoods, then we subconsciously favor the more difficult way we had learned things. That spectre of loss has hung over our human lives since the beginning.

It's likely the source of calling kids lazy, the reason for tribes people who had sent their youth out into the wilderness alone as a rite of passage about survival, the urgency about preparing the next generation in hopes of avoiding the hardships that so easily can happen.

The root of such instinct is perhaps why that professor had started you on indecipherable content.

So when many of us had struggled day and night for years to learn something, we might subconsciously be ok with a material being super difficult for people. With the ongoing spectre of how any person can lose their livelihoods, continually refreshed by reminders, we don't have incentive to ensure the material is too easy to learn.

"Was hard for me, should be hard for them!"

Yet energy efficiency is a powerfully overriding force. Our bodies love things that preserve our energy. So when we invent an easier way, the ones who worked hard on the obsoleted way might complain, then many give in to the ease on their energy.

However, when something is still overly difficult, we have a strong momentum in that direction of maintaining difficulty because of all the energy we invested into overcoming the challenge.

It's simply a matter of job security: if nearly everyone could learn the same skill too quickly, then they won't need us, and what does that mean for our jobs?

We have a similar concern playing out in the world of arts with AI content generation.

So then I imagine, do things have to be that way? If a parallel Earth had redesigned its science to be super easy to learn with an accurate simplicity, so a lot more people are knowledgeable enough about how they might make stuff locally by putting the emerging technologies together with the existing ones in the right ways, could they build and grow their own necessities without having to buy so much from afar?

Great writeup! I read about half and am a slow reader, so will read the rest later in order to finish this post, eat dinner, and get enough sleep for a job tomorrow: part of my livelihood.

I wawant to address two points from your writeup though:

You mention scientists are human like everyone else. That's right.

So far, our conclusions about accuracy in communicating science isn't very scientific.

I want to test it and could use tips to guide a proper set up.

Since it's difficult to be rigorous with subjective human experiences.

But, where there's a will there's a way.

Maybe take a group of people whose knowledge of science is almost zero. There's such people in my own (extended) family so it's more doable than would seem possible.

Teach half of them a physics class how it would've been taught in 1900 with textbooks and dry jargon. (but modern science)

And teach half of them the identical type of physics and maths using extra visuals and immersive animations while replacing any dry jargon with everyday words or an intuitive substitute designed with specific guidelines.

Test the outcome by which class is able to do a successful experiment from what they learned.

Ok good night.
 
  • #14
syfry said:
If a parallel Earth had redesigned its science to be super easy to learn with an accurate simplicity
How would this magically happen? The difficulty of learning accurate science is not up to us; we can't just choose it to be what we want. It is set by nature and how nature works, and we don't control that.
 
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  • #15
PeterDonis said:
How would this magically happen? The difficulty of learning accurate science is not up to us; we can't just choose it to be what we want. It is set by nature and how nature works, and we don't control that.
Was at work and busy, yet thought about how to answer your question. And found it in a reddit post. The top answers are all the same:

Persistence, a lot of work, budgeting one's time, and enjoyment of learning it.

Takes that (and more) to transform and deeply infuse the learning material with an accurate simplicity.

No magic. But the results might seem magical, if only because we apply the principles to learning, but then mostly neglect to apply those for an effective and accurate simplicity.

You quoted the answer. We redesign the science.

Similarly to the above, what it'll take to accurately simplify:

Persistence, a lot of work, enjoy accurately simplifying, budget our time, test the simplified material for effectiveness with random people, then test, test, and (continually) test again all double blind, and do such an effort in an open collaboration.

We could use that and today's technology toward that effort, to the max.

My hypothesis is that people in every academic realm including science consciously want everyone to learn, while subconsciously want to continue having a job for their livelihoods.

So the problem is that in every type of trade and field, technology, science, medicine / healthcare, maths, etc, we lack an incentive to redesign the learning material because we must ensure our own livelihoods.

So that's another area for us to solve.
 
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  • #16
syfry said:
Persistence, a lot of work, budgeting one's time, and enjoyment of learning it.
Sure, this is all good, but none of it makes science simpler than it is.

syfry said:
Takes that (and more) to transform and deeply infuse the learning material with an accurate simplicity.
You are assuming that "an accurate simplicity" is even possible. What if it isn't? What if an accurate presentation of the material is inherently not simple? For example, suppose you can't just understand it right off the bat, you first need to understand fifty or sixty other things that underlie it?

syfry said:
We redesign the science.
I quoted the answer in order to demonstrate its absurdity. We can't "redesign" the science, because we don't get to dictate what the science is. We have to take Nature as it is; we can't declare by fiat that Nature should work in a way that we can understand with "accurate simplicity".

syfry said:
So that's another area for us to solve.
If you really think that what you describe is possible, then I suggest you go and do it. Good luck.
 
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  • #17
syfry said:
And found it in a reddit post.
So you apparently think reddit is a good source for this sort of information. It is to laugh.
 
  • #18
What does happen is, that we occasionally find new mathematical concepts that help to phrase physics better, and more accurately. Both fields have developed in parallel for a long time, and sometimes still do. However, that only transfers one simplicity into the complexity of the other. E.g., Noether's theorem is of physical elegance but requires some hard mathematics to prove it.
 
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  • #19
As James Macneil Whistler said, just a few years before Noether, "Two plus two continue to make four, despite the whine of the amateur for three or the cry of the critics for five."

"You scientists are doing it all wrong! All wrong!" Is something we hear over and over again. The fact that they use technology that depends on this science that is being done so wrongly. As said in another post,
PeterDonis said:
it is to laugh

This is not novel.
 
  • #20
PeterDonis said:
Sure, this is all good, but none of it makes science simpler than it is.
Agreed, that part was the persistence and hard work that the reddit physics sub had said is needed to learn science. I'm claiming an accurate simplicity needs that and possibly more: an epic amount of persistence and work.

To be clear, I'm comparing learning physics as people currently do vs accurately simplifying the way it's taught so that most people can learn it a lot faster.

You are assuming that "an accurate simplicity" is even possible. What if it isn't?
Agreed. We're on the same page that it's to be experimentally verified and shown to be possible.

I quoted the answer in order to demonstrate its absurdity. We can't "redesign" the science, because we don't get to dictate what the science is. We have to take Nature as it is; we can't declare by fiat that Nature should work in a way that we can understand with "accurate simplicity".
Agreed, because I'm defining science as in 'teaching science', not as in 'redesign reality'.

Our standards for the language of science are confusing. We're stuck using outdated wording for things that were named when we misunderstood them, and when a deeper understanding had later showed what's really at play, we often keep the older wording.

We haven't bothered creating an open and collaborative system of updating such outdated language.

We could involve students and teachers to ensure that scientists, teachers, and students are together agreeing on how to reshape the language.

How many people here are involved in any such thing as redesigning how we teach?

My safe bet is that such a thing either doesn't exist (hopefully I'm incorrect about that), or, that if it does exist, it doesn't get the type of persistence and epic effort that it could.

If you really think that what you describe is possible, then I suggest you go and do it. Good luck.

It'll take more than luck.

But yes, I've been working on something.

There'll be many approaches. Ways we can safely redo the entirety of how we teach science and how we phrase its language.

For example, gamifying the effort. In an open collaboration.

One game scenario: we suddenly learn that everyone is vanishing from Earth except the 6 to 8 years old... we must to rethink how to phrase all of the technical phrases and jargon in science and technology, and maths, so that the oldest kids can learn enough to build and run the things on their own purely from our instructions: in written form, spoken, animated, VR glasses, any creative way we dream up.

Another is a sci-fi scenario: inter gliders who travel to parallel Earths after discovering their existence. The gliders find instances of a wording convention on some Earths that would accelerate its learning of science by eliminating a related misconception, for example Earths that might teach at the earliest grade that all things move at the speed of light unless something is reducing that speed, such as interaction of matter with the mass field (so named because Higgs had taken another unrelated career path at many Earths) for most types of matter, such as interaction of light's speed with water, etc. Students there might often avoid the usual errors and mix-ups we experience on our Earth, for example about why inertia exists, or about whether matter can reach the speed of light at this stage of our already cooled universe.

Another series of Earths might've entirely discarded the concept of 'at rest', at least in the minds of students, who instead might learn that everything is in motion, and they are usually in 'synced motion' with a car if they're a passenger, or with a planet if they're on its surface, and so on.

On various Earths, perhaps a spacetime relativity has combined special relativity and general relativity which in those Earths had developed together as a single model, so they weren't thought of as separate.

Now the gamification: the gliders found that one of the Earths had collected all of the best ways to describe science by to shape its language for teaching it much faster. The same with maths.

What does that look like?

We answer that in a collaboration and by testing its effectiveness.

Want to explore what the results are like? Go into a VR world where you can experience a classroom teaching the results at some hypothetical parallel Earth.

Another scenario uses AI to translate any paragraph of science you're reading that's hard to decipher. And you might even translate that into the parallel Earth's collected best.

Now you u might ask, wat use is putting all of this effort into accurate simplicity?

The goal is that everyone can learn science a lot faster.

For example, with today's level of technology, it's unreasonable to expect an isolated tribe in the wilds to learn not only our specific language, but also every specific way we've phrased everything, in order for them to enjoy the power of science knowledge and all it has to offer them.

Science is also powerful for creating and inventing more things locally, if you support local.

Science belongs to everyone.
 
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  • #21
syfry said:
I'm comparing learning physics as people currently do vs accurately simplifying the way it's taught so that most people can learn it a lot faster.
Yes, I'm quite clear about that. I just don't share your optimism about it being possible. I believe it was Euclid who said that there is no royal road to learning. Some things take the time they take.
 
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  • #22
syfry said:
I've been working on something.
Your own personal projects and research are off topic here. If you get something published in a peer-reviewed journal, then it would be a possible topic for discussion in the appropriate subforum of PF.
 
  • #23
syfry said:
Science belongs to everyone.
And everybody can learn it, today easier than ever. That does not mean it can be taught in comic strips. And not all people can learn it equally fast. The trick is to be curious and to know whom to ask! But nobody can learn everything, not even in a single subject area.
 
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  • #24
PeterDonis said:
I believe it was Euclid who said that there is no royal road to learning. Some things take the time they take.
Someone probably said, test all assumptions. Shouldn't we believe the results of testing override what anyone had said, an authority or not?

Until that time, the person's claim might hold weight. And their claim will hold better weight if someone specifically tests it and the results still agree with that person.

But, if the results disagree, and if they would continue to consistently with independent tests, then that potential impact is worth the testing.

Technically, I do agree with the first part of his claim. There isn't a 'royal' road to learning. 🙂
 
  • #25
syfry said:
Someone probably said, test all assumptions.
Yes, that's fine. But you appear to believe that nobody has been doing that in this area. That claim seems to me to be, to say the least, implausible. Particularly today when online learning sites seem to be multiplying like rabbits.
 
  • #26
syfry said:
Our standards for the language of science are confusing.
Maybe before fixing all of science you could fix some other more commonly used terms.

Why do we drive on a parkway and park on a driveway?
How can a job be completely unfinished?
How large exactly is jumbo shrimp?
Can a couple be alone together?
Is this post seriously funny?

When we get those taken care of we can start working on technical terms.
 
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  • #27
PeterDonis said:
Yes, that's fine. But you appear to believe that nobody has been doing that in this area. That claim seems to me to be, to say the least, implausible. Particularly today when online learning sites seem to be multiplying like rabbits.
People are teaching, yes. And they're trying to simplify. Some do great, many are making things almost worse.

I'm going for specific guidelines: first and foremost, double check and triple check with actual scientists to ensure the accuracy. Also, have a consistent structure, not merely all sorts of random ways people choose to simplify. Test the results. Involve the teachers and students. etc.
Vanadium 50 said:
Maybe before fixing all of science you
I cannot do any such thing. That'd be absurd for any person to try.

My approach is to write principles for accurately simplifying the best way that's feasible, with demos as examples and guidelines (testing will show which ways are most effective), based on my ability to teach people stuff I've struggled with a lot faster than usual, dropping all technical wording and substituting in everyday language.

And, it must be an open collaboration by livestream. Open to all, temporarily anonymizing each person to relax the ego a bit.
 
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  • #28
PeterDonis said:
Yes, that's fine. But you appear to believe that nobody has been doing that in this area. That claim seems to me to be, to say the least, implausible. Particularly today when online learning sites seem to be multiplying like rabbits.
Yes, but it also offers gems! Without the internet, I would never have seen Einstein, Noether, Newton, or Gauß in their original versions. I found that more than interesting.

There are literally dozens of university servers in North America and Europe alone with entire curricula available as lecture notes. Even the risk of buying the wrong book or attending a course that is too difficult doesn't exist anymore. Walk over to the next server, to the next language, and find the pdf that fits your level. (Not you as in 'you', of course, more like in 'one'.)
 
  • #29
syfry said:
My approach
Is, as I have already said, off topic here.
 
  • #31
After moderator review, the thread will remain closed as the original question has been addressed and discussion of the OP's personal research project is off topic.
 

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