This question is why measure theory exists.

[0] https://en.m.wikipedia.org/wiki/Lebesgue_measure

[1] https://omnicognate.wordpress.com/2013/11/04/sigma-algebras-...

I can recommend "Calculus: Basic Concepts for High Schools" by the same author (L.V. Tarasov) to anybody unfamiliar with calculus: https://archive.org/details/TarasovCalculus/page/n1/mode/2up. It's written as a dialogue between author and reader.

His book on school physics also use the dialogue approach:

Questions and Answers in School Physics (Dialogues between students and teacher)

https://archive.org/details/questions-and-answers-in-school-...

While other two books use dialogues intermittently as in the probability book

Basics Concepts of Quantum Mechanics

https://archive.org/details/tarasov-basic-concepts-of-quantu...

This Amazingly Symmetrical World

https://archive.org/details/TarasovThisAmazinglySymmetricalW...

(I am the curator/maintainer of the mirtitles.org blog and the typesetter of the books)

There is a point where all of you will finally come to appreciate the limits of rationalism and materialism and let go a bit more.

we only stop because it’s convenient to stop. But that doesn’t make the size of anything have any specific size other than where we stop measuring it.

What you're saying is in the practical real world we can never measure things exactly. That's true but that's not what I got from calculus. Irrational numbers come to mind (not calculus).

I come to almost the opposite conclusion as you. It is amazing that we can solve equations in spite of infinities.

Calculus put a man on the moon and a camera next to Pluto.

I think the OP's point is that much like the Newtonian physics that paired with calculus to put a man on the moon, calculus is a pragmatically magnificent tool that doesn't yield exactly correct or perfectly accurate answers for many questions. Just "enough accuracy for the problem you're solving," in some very real senses.

What you are calling an exact result is only a limit function. All “things” will measure infinitely.

Can it love?

> Calculus put a man on the moon and a camera next to Pluto.

I am not saying the illusion is not useful, but all the things that come out of it are also inside the illusion.

What if Pluto is not as far away as we actually think it is?

The idea of distance being a human construct is not a new idea and may be the underpinnings of spooky action at a distance.

Distance is a human concept. The moment we stop thinking distance does not exist. It may be a limitation that we perceive distance as something to be overcome through rocket ships and not through other methods.

Time is also in the same category. If you want to read a good book on the topic read “the end of Time quote by Jason Barbour.

What if, what if.. um.. nothing, really? Our ships continue to work for a while, (may be t=0), then they won't, and we correct the models or the math.

> This completely digital version typeset in using TEX with EB Garamond font by DAMITR MAZANAV [email protected]

> Released on the web by http://mirtitles.org in 2023.

> Access the BTEX project files http://gitlab.com/mirtitles/twibop

https://archive.org/details/LevTarasovCalculusBasicConceptsF...

Performing a measurement just means you become entangled with the thing you’re measuring.

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

Perhaps this doesn't quite count this as "standard quantum mechanics though. As I understand there is a very tight-knit theory consisting of a mathematical model (Measurements are self adjoint operators on a Hilbert spaces, unitary evolution given bx the hamiltonian, states are unit vectors or POVMs.) together with a physical interpretation that amazingly fits the observations.

This + quantum decoherence seems more in the realm of mathematical theory with a nice interpretation and some experimental evidence.

The many-worlds interpretation is a way to talk away the probability interpretation, unfortunately it is not falsifiable in any way at the moment.

s/universe/multiverse/

And a universe is fundamentally probabilistic.

I watched it a few years ago so may be misremembering bits but I think that is the gist…

Worth a watch especially if you balk at this idea just to to see a strong counter argument.

https://m.youtube.com/watch?v=wfzSE4Hoxbc&t=0s

Edit: link

Light is always a wave, never a particle. And a wave is just a probability.

> probability distributions can have multiple peaks with equal probability?

I think I know where you are going, but can you be more clear so I do not confuse things with my assumptions?

But our mental system is not as perfect. Because a person with schizophrenia or someone on LSD they surely not see the same things we do.

why does the mind only experience one of the brains collapsed states?

The mind doesn’t experience a collapsed state, it is a collapsed state. And from that collapsed state, we experience all other collapsed states through the same brain function.

The brain uses our senses to collect the probabilities that exist in the world, and the brain collapses those probabilities into a single “point”.

[email protected]

Is the address correct, and I have made an error? Perhaps it's .net?

Thank you!

It's the biggest, baddest, hammer in probabilistic machine learning.

The quality of paper used, the typesetting, the cloth binding and in general the physical attributes of their books were a work of art in itself. One can easily fall in love with the physical book just for the way it was designed, let alone the content.

The authors used in their translated works were equally exceptional in their translation.

I fondly remember reading their "Physics for entertainment" by Perelman as a translated work in good old days and it actually made me fall in love with the text book physics taught at the school level.

Given that this was an artifact when USSR made it even more fascinating. Books were priced a trifle over the shipping cost as they were likely subsidized heavily by the government.

It is sad to see that they are no more. They were likely defunded/dissolved when USSR broke up.

Thank you MIR for lighting up my childhood.

RIP.

- https://mirtitles.org/

- https://mirtitles.org/2012/04/30/misha/

https://archive.org/details/mir-titles

IA's browser e-reader is pretty nice to use overall, and the Mir titles seem to have been converted into various downloadable formats as well, in addition to what I'm guessing is the native PDF.

Props to the collection maintainer. This brings back some really good memories.

Note--It seems like some additional Mir books, in various states of curation, may be accessible via IA through search:

https://archive.org/search?query=Yakov+Perelman

You don’t have to guess—the IA metadata tells you which formats were originally provided by the uploader and which ones were derived by IA. The “download original” link on the website uses that, or you can pass --source=origial to the CLI[1].

[1] https://archive.org/developers/internetarchive/cli.html#down...

Thanks for the comment and putting in the perspective. The project started with the idea of preserving this knowledge about 15 years back. I grew up reading those books, but they were nowhere to be found for others to read by the end of 90s. The collection has been a collaborative effort with people from across the globe contributing to it. Though it will take some time (read years/decades), hopefully one day the collection will have all the books published during the Soviet era.

Not the same printing quality, but still decent.

Ah, good old days!

Even into the early 2000s, Springer would often make the first printing of a textbook sewn-bound, then subsequent printings were cheaply perfect-bound. I stopped buying new Springer books online around 2005, because I wanted to check the binding before buying.

1980s AI-chat emulation technology: just print the chat history on a book

But seriously, conversation style feels a lot more natural sometimes than just reading a wall of text and trying to decipher its meaning

Statistics and probability are tools humans use to predict outcomes of the world, they are not necessarily accurate reflections of the mechanisms of the world. Maybe I'm strawmanning the author here, I don't know. I may read the full book at some point but probably not yet.

There may very well be a limit where events are random (such as particle decay), but surely even fully determined events can have probabilistic outcomes, when aggregated. Like say you have 4 beads, 3 black and 1 white. And you non-blindly align all combinations of three beads. You'll have four combinations, three of which contain a white bead. So the probabilistic odds of any one combination of three beads containing a white bead is 75%. If a person picks three beads based on preference, another person can say that there's a 75% chance that those three beads will contain a white bead, iterated over enough picks. But the actual picking for all picks is fully determined by the current preference of the person picking the three beads.

That's not true, which is the critical point, because preference is not independent.

In the world of online gambling, someone who knows the seed of the RNG, game outcome is not random. For others, it is. Here people with computers ARE allowed, because it's much harder to break a cryptographic RNG than to calculate physical roulette biases.