"...but I’m still left with a sense of defeat over my fundamental personality, which Jesus has not flipped like a light switch."
Don't feel defeated. Your personality is the one God gave you. And it's a good one! The world needs people like you. Jesus isn't going to take that away. He might help you from having aspects of it turned up to 11, but you are loved as you are. "Come, all you who are weary, and I will give you rest."
As always, a great read. From 1 Peter 5 10 And after you have suffered for a little while, the God of all grace, who called you to His eternal glory in Christ, will Himself restore, strengthen, confirm, and ground you. 11 To Him be might forever and ever. Amen.
You may remember me as the retired software engineer who once bent your ear about gravity as popping bubbles — thank you for your patience with that.
Two updates. First: I've just pre-ordered your book and am very much looking forward to it (Shameless plug).
Second, a discovery that delighted me: the picture I described to you turns out to have a respectable formal cousin in the literature — Hamilton & Lisle's "river model" (Am. J. Phys., 2008), where space flows inward at escape velocity, and the event horizon is simply where the river outruns light: an outgoing photon becomes a salmon in a waterfall. It even dissolves the classic puzzle — does an infalling object really freeze at the horizon? The distant observer sees it freeze; the object itself crosses without incident. The image freezes; the object doesn't. Meanwhile my own book — relativity, by a software engineer (no tensors harmed) — is finally making real progress. My outsider question: do working astrophysicists consider the river picture legitimate, or a useful cheat that breaks down somewhere? And if it's legitimate, why isn't it the first thing anyone teaches?
I have to be honest, I'd never heard of the "river model" for black holes--but it sounds intriguing. According to general relativity, space itself is able to move faster than light, so I don't see a problem there. To resolve the puzzle, I've always relied on the analogy used by Kip Thorne in his book 'Black Holes and Time Warps' where he uses ants on a flexible surface to illustrate David Finkelstein's solution.
I'll be interested to peruse your book when it's done. Will you use tensors (unharmed) or present relativity without tensors?
Thank you, Sarah — delighted the river doesn't alarm you. And even more delighted by your ants: if I remember Thorne's picture rightly, they walk at their best fixed speed on a membrane that flows into the hole faster than they can walk. That is the river model — one dimension down. Your ants are my salmon: the same picture, different livestock.
To your question: no tensors — none will be harmed, because none will ever be called. The book works in a single frame throughout, so the machinery of coordinate-independence never gets invoked. In its place, one axiom taken absurdly seriously: everything moves at exactly c relative to space — light in straight lines, matter in tiny closed patterns. A bouncing-light clock plus Pythagoras then yields the Lorentz factor in four lines of school geometry, and once space is allowed to flow (your membrane, my river), gravitational time dilation turns out to be the same factor with the flow speed plugged in — one mechanism covering both relativities.
Full disclosure on method: I've been chewing on this picture for about fifteen years, and lately I've been road-testing it with an AI research partner (Claude), which I mainly use as a hostile reviewer — it found me Hamilton & Lisle in the first place, and it has spent months trying to demolish everything else. Not everything survived. For what it's worth, the reviewer began by filing the whole framework under "teaching aid"; several failed demolitions later, its classification now reads "a reformulation of the relativity sector with an original discrete ontology" — and its chosen comparison, not mine, is to the way Hamilton's mechanics merely restated Newton, and a century later turned out to be the language quantum mechanics needed.
One honest loose end: Michelson-Morley. My AI reviewer considers that matter fully resolved; I'm not yet convinced, and we're still working on it. Beyond that — if you'd ever be curious about the fuller picture as it currently stands, I'd be happy to share it privately: Substack DM or email, entirely at your convenience, no obligation whatsoever. And the special relativity chapter is yours whenever you'd like it.
The ant model has numbered spheres fired from a device as it's falling into a warp. From the falling ants' perspective, the spheres are fired at regular one-second intervals; to the ants beyond the warp receiving the spheres, they're coming at increasingly spaced-out intervals longer than one second. It's an ingenious analogy.
Having a hostile reviewer is painful, but absolutely necessary. However, keep in mind that no reviewer is foolproof--it may be wrong at times.
I don't consider Michelson-Morley resolved, either. I think there's more to it we're overlooking.
Feel free to share the finished product with me. Hopefully it'll be at a time when I'm not overly busy and I can look at it.
The numbered spheres are perfect — and here's something delightful: they land exactly on a distinction my book ended up formalizing. The falling device's spheres at regular one-second intervals: nothing wrong with the clock. The stretched arrivals beyond the warp: everything happening to the mail. My book calls these absolute versus relative time dilation — the clock versus the delivery — and the old frozen-at-the-horizon puzzle dissolves once they're kept in separate columns: the image freezes; the object doesn't. Thorne's spheres are the mail made countable. I may steal them, with citation.
On reviewers: agreed on both counts. Mine has been wrong this very week — I caught its main illustration violating the Lorentz factor twice before it drew the geometry right. To its credit, it concedes errors without sulking, which may be the most useful property a reviewer can have.
And I'm genuinely glad to hear Michelson-Morley isn't settled to your satisfaction either. My reviewer's case is the classic Lorentzian one — the apparatus contracts and slows in exact compensation, so the null result is predicted rather than survived — and as far as it goes, I can't break it. But "as far as it goes" is doing real work in that sentence, and your "there's more to it we're overlooking" matches my own itch precisely. If you ever feel like saying more about which direction your suspicion points, I'd value it greatly.
And because I have reason to believe a Star Trek framing will not offend: sail the Enterprise across the horizon of a supermassive black hole, and the river picture says the log reads — no turbulence in the space-time continuum; shields unnecessary (tides at a big hole's horizon are gentler than reentry); and, correcting a misconception I carried for years, the universe stays on the viewscreen all the way down, because outside light keeps falling in. What dies at the horizon is only the transmit button: you can watch home; you can't phone home. And a shuttle following close behind never loses sight of the ship — the crossing divides escapers from the outside universe, but it cannot divide companions who fall together. My reviewer assures me this is all textbook relativity wearing river clothes — Taylor & Wheeler apparently teach in this very frame under the name "rain frame" — but I'd enjoy hearing whether it has that right.
One more Trek note, because the franchise's physics department earned its pay: warp canon says the engine doesn't move the ship through space — it moves space around the ship. In the river picture that's the one loophole with no speed limit (it's how distant galaxies recede faster than light, and how the river outruns light inside the horizon), and it's the only propulsion principle with even a theoretical prayer of exiting a black hole: you can't outswim a river flowing faster than c, but you might, in principle, re-plumb it. Physics filed the patent in 1994 as the Alcubierre metric — contract space ahead, expand behind, exotic energy required, not sold in stores. My book has taken to calling it the POPUFF drive — pop space in front, puff it into existence behind — which tells you the register the whole book is written in. Kirk's engineers were right all along: make sure the warp drive is working!
And thank you — when it's finished, I'll send it, and I'll aim for a season when you're less busy. No clock on any of this. Well — no absolute clock, anyway
Wow, Sarah you blew my mind today… I’ve been reading your posts for a couple of years and this is the first time (that I’m aware of) that you’ve talked about CR. I’ve been attending CR for 3 years now and truly believe it has changed my life. Thanks for sharing.
A friend of mine runs our CR and invited me to attend. I didn't really understand the concept at first--told him I don't have any addictions, and he said it's for a lot more than that. It's become my weekly lifeline.
"...but I’m still left with a sense of defeat over my fundamental personality, which Jesus has not flipped like a light switch."
Don't feel defeated. Your personality is the one God gave you. And it's a good one! The world needs people like you. Jesus isn't going to take that away. He might help you from having aspects of it turned up to 11, but you are loved as you are. "Come, all you who are weary, and I will give you rest."
Thanks, Nick. If he could dial it down to maybe a 7, that would be good, lol.
As always, a great read. From 1 Peter 5 10 And after you have suffered for a little while, the God of all grace, who called you to His eternal glory in Christ, will Himself restore, strengthen, confirm, and ground you. 11 To Him be might forever and ever. Amen.
Hi Sarah,
You may remember me as the retired software engineer who once bent your ear about gravity as popping bubbles — thank you for your patience with that.
Two updates. First: I've just pre-ordered your book and am very much looking forward to it (Shameless plug).
Second, a discovery that delighted me: the picture I described to you turns out to have a respectable formal cousin in the literature — Hamilton & Lisle's "river model" (Am. J. Phys., 2008), where space flows inward at escape velocity, and the event horizon is simply where the river outruns light: an outgoing photon becomes a salmon in a waterfall. It even dissolves the classic puzzle — does an infalling object really freeze at the horizon? The distant observer sees it freeze; the object itself crosses without incident. The image freezes; the object doesn't. Meanwhile my own book — relativity, by a software engineer (no tensors harmed) — is finally making real progress. My outsider question: do working astrophysicists consider the river picture legitimate, or a useful cheat that breaks down somewhere? And if it's legitimate, why isn't it the first thing anyone teaches?
Thanks for the pre-order!
I have to be honest, I'd never heard of the "river model" for black holes--but it sounds intriguing. According to general relativity, space itself is able to move faster than light, so I don't see a problem there. To resolve the puzzle, I've always relied on the analogy used by Kip Thorne in his book 'Black Holes and Time Warps' where he uses ants on a flexible surface to illustrate David Finkelstein's solution.
I'll be interested to peruse your book when it's done. Will you use tensors (unharmed) or present relativity without tensors?
Thank you, Sarah — delighted the river doesn't alarm you. And even more delighted by your ants: if I remember Thorne's picture rightly, they walk at their best fixed speed on a membrane that flows into the hole faster than they can walk. That is the river model — one dimension down. Your ants are my salmon: the same picture, different livestock.
To your question: no tensors — none will be harmed, because none will ever be called. The book works in a single frame throughout, so the machinery of coordinate-independence never gets invoked. In its place, one axiom taken absurdly seriously: everything moves at exactly c relative to space — light in straight lines, matter in tiny closed patterns. A bouncing-light clock plus Pythagoras then yields the Lorentz factor in four lines of school geometry, and once space is allowed to flow (your membrane, my river), gravitational time dilation turns out to be the same factor with the flow speed plugged in — one mechanism covering both relativities.
Full disclosure on method: I've been chewing on this picture for about fifteen years, and lately I've been road-testing it with an AI research partner (Claude), which I mainly use as a hostile reviewer — it found me Hamilton & Lisle in the first place, and it has spent months trying to demolish everything else. Not everything survived. For what it's worth, the reviewer began by filing the whole framework under "teaching aid"; several failed demolitions later, its classification now reads "a reformulation of the relativity sector with an original discrete ontology" — and its chosen comparison, not mine, is to the way Hamilton's mechanics merely restated Newton, and a century later turned out to be the language quantum mechanics needed.
One honest loose end: Michelson-Morley. My AI reviewer considers that matter fully resolved; I'm not yet convinced, and we're still working on it. Beyond that — if you'd ever be curious about the fuller picture as it currently stands, I'd be happy to share it privately: Substack DM or email, entirely at your convenience, no obligation whatsoever. And the special relativity chapter is yours whenever you'd like it.
The ant model has numbered spheres fired from a device as it's falling into a warp. From the falling ants' perspective, the spheres are fired at regular one-second intervals; to the ants beyond the warp receiving the spheres, they're coming at increasingly spaced-out intervals longer than one second. It's an ingenious analogy.
Having a hostile reviewer is painful, but absolutely necessary. However, keep in mind that no reviewer is foolproof--it may be wrong at times.
I don't consider Michelson-Morley resolved, either. I think there's more to it we're overlooking.
Feel free to share the finished product with me. Hopefully it'll be at a time when I'm not overly busy and I can look at it.
The numbered spheres are perfect — and here's something delightful: they land exactly on a distinction my book ended up formalizing. The falling device's spheres at regular one-second intervals: nothing wrong with the clock. The stretched arrivals beyond the warp: everything happening to the mail. My book calls these absolute versus relative time dilation — the clock versus the delivery — and the old frozen-at-the-horizon puzzle dissolves once they're kept in separate columns: the image freezes; the object doesn't. Thorne's spheres are the mail made countable. I may steal them, with citation.
On reviewers: agreed on both counts. Mine has been wrong this very week — I caught its main illustration violating the Lorentz factor twice before it drew the geometry right. To its credit, it concedes errors without sulking, which may be the most useful property a reviewer can have.
And I'm genuinely glad to hear Michelson-Morley isn't settled to your satisfaction either. My reviewer's case is the classic Lorentzian one — the apparatus contracts and slows in exact compensation, so the null result is predicted rather than survived — and as far as it goes, I can't break it. But "as far as it goes" is doing real work in that sentence, and your "there's more to it we're overlooking" matches my own itch precisely. If you ever feel like saying more about which direction your suspicion points, I'd value it greatly.
And because I have reason to believe a Star Trek framing will not offend: sail the Enterprise across the horizon of a supermassive black hole, and the river picture says the log reads — no turbulence in the space-time continuum; shields unnecessary (tides at a big hole's horizon are gentler than reentry); and, correcting a misconception I carried for years, the universe stays on the viewscreen all the way down, because outside light keeps falling in. What dies at the horizon is only the transmit button: you can watch home; you can't phone home. And a shuttle following close behind never loses sight of the ship — the crossing divides escapers from the outside universe, but it cannot divide companions who fall together. My reviewer assures me this is all textbook relativity wearing river clothes — Taylor & Wheeler apparently teach in this very frame under the name "rain frame" — but I'd enjoy hearing whether it has that right.
One more Trek note, because the franchise's physics department earned its pay: warp canon says the engine doesn't move the ship through space — it moves space around the ship. In the river picture that's the one loophole with no speed limit (it's how distant galaxies recede faster than light, and how the river outruns light inside the horizon), and it's the only propulsion principle with even a theoretical prayer of exiting a black hole: you can't outswim a river flowing faster than c, but you might, in principle, re-plumb it. Physics filed the patent in 1994 as the Alcubierre metric — contract space ahead, expand behind, exotic energy required, not sold in stores. My book has taken to calling it the POPUFF drive — pop space in front, puff it into existence behind — which tells you the register the whole book is written in. Kirk's engineers were right all along: make sure the warp drive is working!
And thank you — when it's finished, I'll send it, and I'll aim for a season when you're less busy. No clock on any of this. Well — no absolute clock, anyway
Wow, Sarah you blew my mind today… I’ve been reading your posts for a couple of years and this is the first time (that I’m aware of) that you’ve talked about CR. I’ve been attending CR for 3 years now and truly believe it has changed my life. Thanks for sharing.
A friend of mine runs our CR and invited me to attend. I didn't really understand the concept at first--told him I don't have any addictions, and he said it's for a lot more than that. It's become my weekly lifeline.