Have we found enough puzzle pieces to get a big picture.

[GaryV]

The number of competing theories has always intrigued me.  When I started reading and studying, it always annoyed me to see professionals say, "we don't understand it.  We just know that is the way it is."  It always seemed like a defeatist attitude.  I made it my mission to learn every theory I could and try to piece together the big picture.  After twenty years, I have created a picture where the extra dimensions of String Theory explain parts of Relativity.  The quirks of Relativity explain the effects of Quantum Mechanics, and more, in an M-Theory style concept.  However, I cannot find anyone who is willing to consider such a wide ranging concept.  I really want to see this studied formally because I have seen some successes with it.  Some of the conclusions I have drawn from my concept have paralleled recent findings that have had nothing to do with me.  For example, a concept that uses the fact that Relativity does not exclude time travel as both an explanation of QM effects and as a physical mechanism for Relativistic mass attenuation.  My conclusion mirrored perfectly the recent confirmation of Color Glass Condensate by the LHC, even though I had written my concept before the article about the CERN result.

My question is, is it possible that we have found enough puzzle pieces to get a big picture, but haven't yet found the perspective?  Also, how does an amateur like me find someone to work with?

[StringJunky]

At the science deep end, if you aren't fluent in the required mathematical language nobody, professionally, will give you the time of day. Verbal or visual descriptors won't cut it with them.

Edited April 29, 2020 by StringJunky

[Phi for All]

27 minutes ago, GaryV said:

When I started reading and studying, it always annoyed me to see professionals say, "we don't understand it.  We just know that is the way it is."

I've been here at SFN for 16 years now, and I've never heard a professional scientist say this. Plenty of them can say, "We don't know", but none of them is willing to let faith ("We just know that is the way it is") be the explanation for any phenomena.

What "competing theories" are you talking about here? Just an observation, but you don't write like someone who has studied and understood these concepts for 20 years. You write like someone who has picked up bits from popular science articles, but lacking formal science study (something I'm guilty of as well), you've used your imagination to stitch together the parts you understand with stuff that just makes sense to you. It's pretty common, but it's a horrible way to learn science. You assume it needs fixing simply because you don't understand it. Asking questions is much better than guesswork.

[MigL]

But you can at least post your 'perspective', listen to any and all criticism that is offered up by members, ask questions about unfamiliar concepts, and learn from the experience.

[GaryV]

I have heard that, and understanding it.  However, I find it extremely short sighted.  All the best breakthroughs came from insights through analogies.  In all the descriptions of Einstein I read, his insights stopped being useful when he delved deeply into the mathematics.

Why couldn't someone like me, be paired with a master of mathematics?  I would provide the insights, and he/she would find the math to describe it.

Phi for all, unfortunately all I have (after my engineering degree) is popular books.  I can't afford to go back.  However, since I have been seeing my conclusions paralleled by real work, it tells me I am on the correct path.  I have also been invited to a NASA conference and a neuroscience conference based on my concepts that were equally developed.  In the past I tried to write more properly.  I got responses from professionals, but many got angry when they found out I was an amateur.  The other amateurs said I was talking over their heads.

[Phi for All]

3 minutes ago, GaryV said:

All the best breakthroughs came from insights through analogies.

I doubt that highly, given their very limited application. I've seen some major misunderstandings stem from taking analogy too far.

5 minutes ago, GaryV said:

In all the descriptions of Einstein I read, his insights stopped being useful when he delved deeply into the mathematics.

This is some heavy confirmation bias against maths, I suppose. I can sympathize, but when in Rome, you should speak Italian, or Latin.

And btw, Einstein got better grades in Algebra and Geometry than he did in Physics. What I remember reading was that Physics only took him so far, and he had to go back to Maths to shore up his best works.

11 minutes ago, GaryV said:

Why couldn't someone like me, be paired with a master of mathematics?  I would provide the insights, and he/she would find the math to describe it.

Where's that Bingo card....

[Ghideon]

14 minutes ago, GaryV said:

 In all the descriptions of Einstein I read, his insights stopped being useful when he delved deeply into the mathematics.

When Einstein delved into mathematics he produced for instance e=mc2, a useful piece of mathematics in my opinion. 

 

49 minutes ago, GaryV said:

After twenty years, I have created a picture where the extra dimensions of String Theory explain parts of Relativity.  

May we see that picture?

 

15 minutes ago, GaryV said:

 I would provide the insights, and he/she would find the math to describe it.

Can you provide the insights in such a way that it makes sense to try to apply mathematics to them?

Edited April 29, 2020 by Ghideon

[Strange]

1 hour ago, GaryV said:

When I started reading and studying, it always annoyed me to see professionals say, "we don't understand it.  We just know that is the way it is."  It always seemed like a defeatist attitude.

I don't think it defeatism; it is an opportunity to study and learn more.

1 hour ago, GaryV said:

I made it my mission to learn every theory I could and try to piece together the big picture.

I hope you have learned them in full mathematical detail, otherwise you have wasted your time.

1 hour ago, GaryV said:

 After twenty years, I have created a picture where the extra dimensions of String Theory explain parts of Relativity.  

Well, the whole point of string theory is that it incorporates relativity. So that is not really a novel idea.

1 hour ago, GaryV said:

The quirks of Relativity explain the effects of Quantum Mechanics

I'm not sure what you mean by "the quirks of relativity". Can you be more specific? And also how it relates to quantum theory?

Are you talking about the fact that quantum field theory combines mechanics and special relativity? if not, how does your idea relate to this?

1 hour ago, GaryV said:

 I really want to see this studied formally because I have seen some successes with it.  

What success? Can you give us examples of quantitative predictions that match experiment or observation?

1 hour ago, GaryV said:

My conclusion mirrored perfectly the recent confirmation of Color Glass Condensate by the LHC, even though I had written my concept before the article about the CERN result.

Maybe you should have published in a scientific journal, then.

39 minutes ago, GaryV said:

All the best breakthroughs came from insights through analogies.

There may be a little bit of truth in that: Newton and the falling apple, Kekule dreaming of a snake eating its own tail and coming up with the structure of benzene. But this only works when it is an expert making the analogical reasoning. 

If you had gone to Kekule and said, "maybe benzene is like a chimpanzee eating a banana, because that makes sense to me" it would not have helped at all.

39 minutes ago, GaryV said:

 In all the descriptions of Einstein I read, his insights stopped being useful when he delved deeply into the mathematics.

Definitely not true.

39 minutes ago, GaryV said:

Why couldn't someone like me, be paired with a master of mathematics?  I would provide the insights, and he/she would find the math to describe it.

Why would they? I'm sure someone with the necessary mathematical skills would have plenty of their own ideas to try out mathematically. Ideas are easy. It is the detail and testing that requires inspiration and hard work.

 

1 hour ago, GaryV said:

My conclusion mirrored perfectly the recent confirmation of Color Glass Condensate by the LHC, even though I had written my concept before the article about the CERN result.

I would not say "confirmed"

Quote

The new observation suggests the collisions may have produced a new type of matter known as color-glass condensate.

...

the CMS collaboration plans to do several weeks of lead-proton collisions, which should allow them to establish whether the collisions really are producing a liquid, Roland says. This should help narrow down the possible explanations

http://news.mit.edu/2012/lead-proton-collisions-at-large-hadron-collider-yield-surprising-results-1127

[studiot]

2 hours ago, GaryV said:

I made it my mission to learn every theory I could and try to piece together the big picture.

This thread isn't really a speculation, more of a personal statement so here are a couple of thoughts I have picked  along the way plus a suggestion or two.

I have read somewhere that the last man alive capable of knowing and understanding 'the big picture' was Archimedes.
After him (he wasn't history's greatest genius) no man or woman had the capacity to look in every corner of Science, it had become just too vast.

Of the many geniuses that follwed him I would place Newton at the top simply because he had not only to invent the Science he also has to invent the necessary Mathematics to go with it.
Einstein at least has the luxury of better mathematicians to help him.

OK, gloom and doom over here are a couple of suggestions.

You do not need journalistic 'popsci' books, there are not many good ones and an engineering degree is already beyond them.

You could try to follow Peter Collier, author of "A Most incomprehensible thing" ; Peter, like yourself, was a man who wnated to know more (about Relativity and Cosmology) so he set himself the task of learning the big picture as it applied there. It is a good read. He has to teach himself the maths of things like tensors to do this.

But that is still a small corner of Science.

A book your background should enable you to access is

Molecular Quantum Mechanics by Professors Atkins and Friedman.
The interesting thing is that they are Professors of Chemistry.
Yet they develop relativistic QM, Group theory, Symmetry theory, explaining the necessary maths as they go along.
It is the nearest thing to  big picture that I know.

 

 

[Strange]

16 minutes ago, studiot said:

I have read somewhere that the last man alive capable of knowing and understanding 'the big picture' was Archimedes.
After him (he wasn't history's greatest genius) no man or woman had the capacity to look in every corner of Science, it had become just too vast.

I have read similar statements about 19th century scientists. Either way, it is certainly true that modern science (even just modern physics, chemistry or biology) is too big for anyone to have a reasonable understanding of all of it.

17 minutes ago, studiot said:

Of the many geniuses that follwed him I would place Newton at the top simply because he had not only to invent the Science he also has to invent the necessary Mathematics to go with it.

When to comes to "inventing science" he was definitely standing on the shoulders of giants. Certainly back to Roger Bacon in the 13th century, Al-Biruni in the 11th and all the way back to the Egyptians and Sumerians.

 

[GaryV]

Ghideon

To give you the full picture, I would need several pages.  However, I will try to condense it.  Afterward, if you are interested, e-mail me and I will send you some PDF's

The fabric of space-time is a fluid in a fourth dimension of space.  The "molecules" of this fluid are represented as the curled up dimensions of String Theory.  Matter in our four dimensional space is an energy wave in the extra dimensional fluid.  Space-time has a resonance equal to the Planck Energy.  Any part of the energy wave that is greater than (and a multiple of) the Planck Energy manifests as a particle in our four dimensional space.  

The universe as a whole began with the creation of a black hole in another universe.  That black hole is a highly spinning, toroidal black hole.  While our space-time is not inside it, it is tied to it.  The rotation of the black hole, and the fact that all space-time is bent back on itself inside a black hole, means that our universe is as such.  The space itself is not curved back on itself, but the progression of time is.  This means our universe is cyclical.  As each iteration begins, time moves slowly, then rapidly increases.  Eventually the flow of time will begin to slow until it stops.  Then it will reverse and the universe will collapse inward.  This explains the missing anti-matter.  Matter and anti-matter is the same, with time flowing in opposite directions.  The missing anti-matter is on the other side of the looped time of our universe.  With respect to the initial universe and its black hole, both were created at the same time, however, anywhere in out universe we will only see matter.  If you were to calculate this probability, and plot the curve, you could see how the universe would appear to change its rate of expansion with respect to the previous part of the curve and find where we would be on this curve.  Then you could predict the age of our iteration and see how it line up with accepted estimates.

Because Relativity permits time travel, but we cannot do it, explains how Relativistic Mass attenuation works.  As elementary particles gain energy, they will be kicked above the speed of light and move backward in time for a short distance as the extra energy dissipates.  Then they would return to normal.  From our perspective, we would see an anti-matter particle appear, move toward the original matter particle and annihilate.  Because this will, for a short time, mean that there are more particles in a given space-time, the more energy mass absorbs, the more mass it will have.  This means that all complex matter will not be able to move faster than light because it will constantly gain mass as Relativity predicts. Someone could calculate the rate of attenuation based on this concept and see if it agrees.  This concept should look just like what the LHC saw as they recorded the color glass condensate.

This is not everything, but I hope this also answers your question, "Can you provide the insights in such a way that it makes sense to try to apply mathematics to them?"

[Strange]

4 minutes ago, GaryV said:

Because Relativity permits time travel

Does it? Only under physically unrealistic scenarios.

4 minutes ago, GaryV said:

explains how Relativistic Mass attenuation works

"Mass attenuation"?

5 minutes ago, GaryV said:

This is not everything, but I hope this also answers your question, "Can you provide the insights in such a way that it makes sense to try to apply mathematics to them?"

I guess part of my problem with all this is that you have taken the results of existing highly mathematical theories, stirred them around a bit, and then expect someone to come up with a mathematical description.

But you are only be able to propose these ideas because a mathematical model exists already. So we are just going round in circles.

That, and the fact that your description makes no physical sense. It seems to be based on a stretching some poor analogies (as used in popular science articles) to breaking point.

Foe example: "the fabric of space-time" there is no "fabric". It is just a misleading analogy. Space-time is just a set of measurements. You might as well say that the "fabric of latitude and longitude is a fluid". Space-time has no more physical reality than latitude and longitude.

And "space-time has a resonance equal to the Planck Energy" doesn't seem to make much sense. Resonance usually applies to frequency; energy is not frequency. And why Planck energy? And you are saying that space-time has a resonance equal to the energy of about half a ton of dynamite (or two average lightning flashes): shouldn't that be easily detectable, somehow? Should we expect lightning to change space-time?

22 minutes ago, GaryV said:

That black hole is a highly spinning, toroidal black hole.

Are toroidal black holes even possible? 

And where is this black hole? How large is it? Would we be able to detect it? What properties does a toroidal black hole have?

22 minutes ago, GaryV said:

While our space-time is not inside it, it is tied to it.

What does "tied to it" mean?

23 minutes ago, GaryV said:

This means our universe is cyclical

This is possible, purely based on the concept of gravity slowing expansion and causing the universe to collapse again. It doesn't require the invention of non-physical black holes.It used to be one of the favoured models (the "big bounce").

But the discovery of dark energy makes this scenario look less likely.

Quote

Someone could calculate the rate of attenuation based on this concept and see if it agrees.

I'm not sure what "attenuation" means here. Not how it could be calculated from the previous description. Nothing is quantified: "elementary particles gain energy, they will be kicked above the speed of light and move backward in time for a short distance as the extra energy dissipates"

How much energy do they gain?

How are they kicked above the speed of light? (When we know this is impossible)

How far backward in time?

How does the energy dissipate?

How much energy dissipates?

And I can't see any connection between this and quantum chromodynamics (color glass condensates).

 

[Ghideon]

1 hour ago, GaryV said:

That black hole is a highly spinning, toroidal black hole.

Closest thing I know of is a Kerr black hole but that is not toroidal. 

1 hour ago, GaryV said:

Because Relativity permits time travel,

Not according to the math I know of.

1 hour ago, GaryV said:

This is not everything, but I hope this also answers your question, "Can you provide the insights in such a way that it makes sense to try to apply mathematics to them?"

For the reasons above I have to say that it unfortunately does not answer that question. Your description suggests at least two concepts that does not seem to make sense according to the mathematics of General Relativity. 

[GaryV]

Look.  I don't now, nor have I ever, claimed to have discovered anything new.

There are two ways to do Physics.  One is to have an insight, then do the math to prove it.  The other is to purely do the math.  I have read dozens of books, seen dozens of documentaries, and seen dozens of interviews.  The one thread that keeps coming out, but is never easy for people to admit (most, not all.  Some do admit it and I respect them for it) is that there are many areas where the math and test prove the theory correct, but we don't understand why or how. Yes I am paraphrasing heavily.  

All I am trying to do is provide a plausible physical mechanism for what is not understood.  That way, someone smarter can take the math to the next level.

[Strange]

1 hour ago, GaryV said:

There are two ways to do Physics.  One is to have an insight, then do the math to prove it.  The other is to purely do the math.

No. There is one way: understand the physics (and therefore the mathematics) and have an insight to develop the field.

1 hour ago, GaryV said:

All I am trying to do is provide a plausible physical mechanism for what is not understood.

You can't provide a plausible physical mechanism if you don't understand the physics.

Several, if not all, of the things you seem to want to explain are already well understood.

I am not aware of a single case of someone who knew nothing about the subject suggesting a new concept that lead scientists to develop new theories. I would love to hear of some, if there are any.

The nearest I can think of is the Mpemba effect. Which, interestingly, is still not understood. But that was more a case of someone making an observation that had been overlooked before. Which is possibly related to the fact that the areas where amateurs can (and do) make significant contributions are astronomy and botany/zoology, which are heavily observation based.

[StringJunky]

5 hours ago, GaryV said:

I have heard that, and understanding it.  However, I find it extremely short sighted.  All the best breakthroughs came from insights through analogies.  In all the descriptions of Einstein I read, his insights stopped being useful when he delved deeply into the mathematics.

Why couldn't someone like me, be paired with a master of mathematics?  I would provide the insights, and he/she would find the math to describe it.

Phi for all, unfortunately all I have (after my engineering degree) is popular books.  I can't afford to go back.  However, since I have been seeing my conclusions paralleled by real work, it tells me I am on the correct path.  I have also been invited to a NASA conference and a neuroscience conference based on my concepts that were equally developed.  In the past I tried to write more properly.  I got responses from professionals, but many got angry when they found out I was an amateur.  The other amateurs said I was talking over their heads.

I think you are misinterpreting this and I have read this. I just think he had his great years then ran out of intuition; fruitlessly seeking hope and clues for inspiration in the maths in his later years. Maths is a tool, not the source of answers but its importance cannot be understated and it is absolutely essential when ones intuition comes up trumps. Scientific ideas are spineless without it.

Edited April 29, 2020 by StringJunky

[Phi for All]

1 hour ago, GaryV said:

All I am trying to do is provide a plausible physical mechanism for what is not understood.

It only seems plausible to you because you made it up from things YOU misunderstood. My evidence? Go back and read where the members have corrected your science. 

6 hours ago, GaryV said:

Phi for all, unfortunately all I have (after my engineering degree) is popular books.  I can't afford to go back.  However, since I have been seeing my conclusions paralleled by real work, it tells me I am on the correct path.  I have also been invited to a NASA conference and a neuroscience conference based on my concepts that were equally developed.  In the past I tried to write more properly.  I got responses from professionals, but many got angry when they found out I was an amateur.  The other amateurs said I was talking over their heads.

How do you, an engineer, justify building on a poor foundation? You can certainly afford Khan Academy for maths and physics. And I really only say this because I don't think your approach is healthy. You have a chip on your shoulder about certain aspects of your knowledge that keep you from successfully filling the gaps in it. 

You should attend those conferences. I got a chance a few years back to go to the International Astronautical Congress and it was amazing. 

I've said this before to many smart people like you. It's a misconception that scientists aren't dreamers and inspired thinkers, that they just plod along with their maths and their experiments. Much of what you may think is not understood is due to working with theory rather than proof. Theories aren't answers, they can be improved. What you're doing is taking bits you've learned (many from pop-sci, where they take objectivity and rigor and replace it with misleading vividness and emotional buzzwords) and using them like paving stones to create a path you can take to your conclusions. That's what you're supposed to do, but without the interconnecting information, you've stopped placing the stones next to each other. Now you're putting them farther and farther apart and taking bigger and bigger leaps to reach your conclusions. You think it's intuitive but it's really non-rigorous and makes large assumptions (toroidal black holes, time travel). Does that make sense? A limited analogy, certainly, but one that resonates, I hope.

 

[cladking]

The problem with our reductionistic perspective is that it's unlikely we can put it all together until we have nearly every piece of the puzzle and we're a very long way from that.   

Even now massive pieces of the puzzle aren't even recognized as being relevant and all the (fractal) corner pieces and most of the edge pieces are missing.   

Reality is logic as is mathematics so there is hope even in the short run.   

[MigL]

Don't let the 'negativity' discourage you.
This is nothing compared to what most Physicist ( any scientists ) face in peer reviews of their work.

Regarding the parts that have been corrected, or dismissed, by forum members, ask questions, such as
"What does the accepted science say ?"
And clarify your non-standard terminology.
Four dimensional space-time is not a 'fabric', but a co-ordinate system which allows for spatial/temporal measurements, and its dimensions are degrees of freedom. In which case, the space-time 'fluid', made up of compacted Calabi-Yau manifolds, is non-sensical.
Asking how the compacted dimensions of string theory manifest themselves, would lead to better understanding and possibly, modifications to your hypothesis, as currently it is not a model or theory

[Mordred]

Ok to to OP. As a professional physicist I can tell you that no descriptive only approach will ever be accepted as a theory.

Lets take the term "compactify a dimension ".

What does a physicist mean or even a mathematician mean by that term.

To answer that question you must first define the word dimension.

Any independent variable or other mathematical  object such as a function, matrix, tensor or group.

So space has three independent variables to define position. {x,y,z} each of these values can change without changing the other value.

So let's take the dimension x described by the set of Real numbers. Uh oh we have a problem.

This set is infinite. We don't like infinite groups or sets in physics. 

So let's compactify (make this set finite)

All infinite groups contain a finite set. So we can compactify this dimension by restricting the set to the applicable finite portions.

Now apply the definition I gave of dimension under mathematics  and subsequently physics to String theory when one states String theory uses day 14  compact dimensions. What he is really saying I have 14 effective degrees of freedom Ie 14 independent variables that are all compactified into finite sets. 

Strings are compactified by the Direchlet and Neumann boundary conditions Ie open strings by the former and the latter for closed strings. All strings describe waveforms.

They are not little objects or matter constituents they describe particle wavefunctions. Each particle has a set number of degrees of freedom. Ie charge, spin, etc etc.

String theory follows all the rules of GR with regards to spacetime and uses precisely the same transformation rules. One of the best lessons I learned to understand invariance under SR came from a string theory textbook.

How to compactify the set [math]\mathbb{R}^4[/math] into the light cone gauge.

Properly studied one will learn that a String corresponds to the action of a point particle. Ie you will need to understand Langrangian action in order to understand Polowskii action or Nambu Goto action.

https://en.m.wikipedia.org/wiki/Nambu–Goto_action

Note the part describing Parameter space....

We describe a string using functions which map a position in the parameter space. This is your extra dimensions

Edited April 30, 2020 by Mordred

[Mordred]

Let's put this into perspective. You want someone to do the math for you.

Ok so would you understand the statement.

The first property in the definition of a Calabi-Yau manifold. X is compact if every collection of sets

[math]V_j\in\tau[/math] which covers X ie [math] X=U_jV_j[/math] which has a finite subcover. If the index j runs over finitely many sets then this condition is met. If j runs over infinitely many sets. This would require that there exists a finite subcollection of sets...

 

This is an example of compactification for the topological spaces used in Calabi-Yau manifolds. Source being String Theory on Calabi-Yau manifolds by Brian R Green.

Can possibly understand that statement without understanding differential geometry and holonomies of topological spaces ?

https://en.m.wikipedia.org/wiki/Topological_space

https://en.m.wikipedia.org/wiki/Hausdorff_space

https://en.m.wikipedia.org/wiki/Holonomy

https://en.m.wikipedia.org/wiki/Parameter_space

https://en.m.wikipedia.org/wiki/Configuration_space_(mathematics)

https://en.m.wikipedia.org/wiki/Phase_space

The following links above all involved in the example I gave.

Edited April 30, 2020 by Mordred

[Ghideon]

7 hours ago, Ghideon said:

Not according to the math I know of.

I'll clarify that a little: Not according to the mathematics supported by observations I know of. 
The Gödel metric allows the existence of closed timelike curves that would seem to allow time travel. But it would require a universe with no Hubble expansion, so it is not a realistic model according to the best available observations.

6 hours ago, GaryV said:

One is to have an insight, then do the math to prove it.

I would change that to something like: "One is to have an observation, then do the math that explains and predicts it." 

 

6 hours ago, GaryV said:

All I am trying to do is provide a plausible physical mechanism for what is not understood.

Using the puzzle analogy from your title: Your description seem to require rearrangements or modifications of the existing pieces in the puzzle until they do not fit together anymore. The result contradicts currently well established theories and observations instead of adding insight and explanations.

 

[Markus Hanke]

3 hours ago, Ghideon said:

The Gödel metric allows the existence of closed timelike curves that would seem to allow time travel. But it would require a universe with no Hubble expansion, so it is not a realistic model according to the best available observations.

 

The Gödel metric does not describe the universe we find ourselves in, so it is not really a relevant cosmological solution to the field equations, though it is of academic value.
So far as CTCs are concerned, they do also occur in solutions that are much more relevant to us - such as the Kerr metric for example. What I would say here though is that the Kerr metric is an idealised solution, in that its precise boundary conditions are not actually physically realisable. Whether or not that has implications for the presence of CTCs, I don’t know.

On a more general level, though allowed by General Relativity, I have would have some fundamental concerns about CTCs. Most notably, in a region of spacetime containing CTCs, the notion of time ordering becomes undefinable, meaning that the evolution of quantum fields and the dynamics of their interactions are no longer unitary. Violations of unitarity are generally a big red flag, and point to something not being right. If I was to hazard a guess, then I would say that topological artefacts such as CTCs only appear in the theory because it is purely classical. Once we have a better understanding of how gravity behaves in the quantum domain, I bet such anomalies will no longer occur.

[Strange]

!

Moderator Note

I have split the discussion of compactificationizering off to here: https://www.scienceforums.net/topic/121967-compactification-split-from-have-we-found-enough-puzzle-pieces-to-get-a-big-picture/