The World is Built on Probability (1984)(archive.org)
archive.org
The World is Built on Probability (1984)
https://archive.org/details/lev-tarasov-the-world-is-built-on-probability-mir-2023
93 comments
I am the curator/maintainer of the mirtitles.org blog and the typesetter of the books.
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.
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.
I find the blog format a bit confusing. Is there a complete listing of the books somewhere?
Just read The tale about the snowflake that did not melt. Lovely little story. Thank you for sharing all this bounty!
Since the linked book is at archive.org: I noticed that it is part of the _Mir Titles_ collection there:
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
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
> [T]he Mir titles seem to have been converted into various downloadable formats as well, in addition to what I'm guessing is the native PDF.
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...
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...
I wish someone would translate Fichtenholz's series on calculus ( https://en.wikipedia.org/wiki/Grigorii_Fichtenholz ). They are the best calculus textbook I've ever read, and they really helped me to master calculus.
The construction of MIR titles reminds me a lot of older Springer GTM and Grundlehren der Mathematischen Wissenschaften series titles. I have a number of Springer titles I've picked up over the years and the older printings were beautifully typeset and bound with very good paper. I try to find the older printings of Springer books when I can when chasing down a copy for my personal library.
Springer books were beautifully typeset until they started having authors do their own typesetting. That's one of the mixed blessings of LaTeX.
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.
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.
Interesting, I must have lucked out quite often and got the first printing back in the mid to late 2000s since back then virtually all of my print Springer books I bought back then were sewn-bound.
I spent several weekends in school trawling through second-hand bookshop backrooms trying to find MIR books in that cloth bound thick paper versions..I still have the I F Sharygin book on plane geometry I found that way.
Ah, good old days!
Ah, good old days!
Dover still publishes lots of translated MIR books.
Not the same printing quality, but still decent.
Not the same printing quality, but still decent.
I read the preface and there are things I agree with and things I find problematic depending on how the author goes about explaining them. The major one of these last is the seeming identity of probability with randomness.
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.
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.
The book discusses the two sources of randomness early on: unknown information and true randomness. It even identifies Democritus and Epicurus as the philosophers who first identified these sources of randomness.
Thank you. I look forward to reading it now.
> 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.
That's not true, which is the critical point, because preference is not independent.
That's not true, which is the critical point, because preference is not independent.
Preference among multiple unrelated people is, at least hypothetically, independent.
“… they are not necessarily accurate reflections of the mechanisms of the world.”
I would suggest taking a few courses on Quantum Mechanics. ;)
Not about this book in particular, but I wanted to thank you for creating this amazing resource. As someone who obsessively bought every MIR title he could while growing up in Delhi, do take a bow.
Seems like a lot of effort went into typesetting this, wow!
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.
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.
Thanks for linking Calculus book.
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)
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)
This seems to have the hallmarks of LaTeX, meaning: not as much time sunk into "typesetting" as you might think ;)
It's not polite to accuse people of not reading the article, but
> 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
> 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
Needs LuaTeX to create. I look forward to learning some TeX typesetting tricks from this.
Learning calculus in high school made me question everything. You can never measure anything, never mind the area of a circe using calculus. It will only ever be a "good enough" measurement.
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.
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.
You seem to have misunderstood the essence of calculus. Calculus provides efficient, high quality estimates for messy real world phenomena.
Calculus put a man on the moon and a camera next to Pluto.
Calculus put a man on the moon and a camera next to Pluto.
> Calculus provides efficient, high quality estimates for messy real world phenomena.
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?
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?
Generally we think things are far away when it takes a longer time to get to them. We have some reasonable assurance that the speed of light is immutable and so we can measure the distance in our frame of reference by bouncing light off of Pluto. Are you nerd sniping sir?
I am making the distinction of what we perceive to be reality to actual reality.
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.
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 Pluto is not as far away as we actually think it is?
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.
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.
You have moved deeply out of the realm of the scientific, into pure imagination. What if squiglal butterplotz mishric?
It’s an imagination where new discoveries are found.
The idea of distance being a human construct is not a new idea and may be the underpinnings of spooky action at a distance.
The idea of distance being a human construct is not a new idea and may be the underpinnings of spooky action at a distance.
Then once you imagine it and write it down in a testable prediction, get back to is. Before then you have no means of getting us here to there.
I have thought it was interesting that, Christians believe, God became human and of all the things in the universe he could choose to teach about, apparently more than anything it is all about love (of a particular kind, actually).
I think OP understands that calculus is an enormously powerful tool.
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.
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.
Huh, what are we talking about here? Calculus does give exact results. What questions are we talking about? Fundamentally statistical questions are going to have inherent uncertainties, its got nothing to do with Calculus.
Calculus make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit.
What you are calling an exact result is only a limit function. All “things” will measure infinitely.
What you are calling an exact result is only a limit function. All “things” will measure infinitely.
Still not understanding what your issue is with calculus. I think so far you only have a problem with its outcomes when you feed it garbage. We expect to see "Calculus" diverge when integrating near the lattice spacing. I don't think we wholly disagree but I am doubtful you are going to make headway fighting against calculus.
I don’t have a problem with calculus, I’m just expressing its limitations. Using calculus to know the area of a circle is useful but it never really measures the area of a circle because the area of any circle is infinite.
It is not really about measuring things, but about reaching a definitive answer given some assumptions. Sometimes our notation of numbers get in the way of writing things shortly (instead of infinite decimal places), other times we can use a fraction and be exact on the paper we write on.
If you can infinitely divide a ruler, you can measure nothing.
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.
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.
I would say calculus is about solving things exactly using infinitesimals and limits. There's also plenty of equations that can only be solved numerically.
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.
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.
I've been meaning to read up on Frank Ramsey, an early 20th century philosopher, mathematician, and economist, who first postulated that people's actions are determined by the balance between their expectations and their desires. A world built on probability would be up his alley, I imagine.
Ramsey is one of those great what-ifs in my mind - just seeing his intellectual output and knowing he died at 26...what would he have given us if he lived a normal life span?
The wavefunction is deterministic. If you take the MWI as the most straight forward interpretation of the math, then the universe if fundamentally deterministic. Probability on a physics level would represent our ignorance of the other branches.
I don't think you can reason like this. As far as I understodod, standard quantum mechanics does not make any statement about how the measuring process and the collapse of the wavefunvtion happens. So while the waveform evolves deterministically, you can only ever apply this model when you are in the position of performing measurements on some quantum mechanical system. As I understand, Quantum mechanics is not meant to also model you together with the experiment as a wavefunction, because the act of you performing a measurement does not have a definition in the form of the wavefunction interacting with itself somehow. So without extensions to QM, you should not reason with universal deterministic waveforms.
> the act of you performing a measurement does not have a definition in the form of the wavefunction interacting with itself somehow
Performing a measurement just means you become entangled with the thing you’re measuring.
https://en.m.wikipedia.org/wiki/Quantum_decoherence
Performing a measurement just means you become entangled with the thing you’re measuring.
https://en.m.wikipedia.org/wiki/Quantum_decoherence
I didn't know that quantum decoherence tackles the measurement problem. It seems like quite an intuitive explanation and does preserve a global wavefunction.
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.
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.
And the thing you're measuring is already entangled with the messy universe around it...
The argument is that the experimental device and you are made up of the same quantum stuff that you're measuring, so there's no reason to suppose a collapse of the wavefunction or that the wavefunction doesn't apply to the entire experimental setup. Just saying if MWI is the correct interpretation.
> then the universe if fundamentally deterministic
s/universe/multiverse/
And a universe is fundamentally probabilistic.
s/universe/multiverse/
And a universe is fundamentally probabilistic.
What i remember from my PDE class was a lecture which involved solving the wave equation for a particular bounded case and, with a slight transformation, the professor showing that the normal distribution was embedded in that solution.
[deleted]
Or it would characterize the futures of the current branch.
Simplicity of mathematical models at the expense of falsification… who needs science, anyways?
David Deutsch’s “Physics Without Probability” covers the history of probability, it’s legitimate and misconceived uses and concludes that according to MWI there is no such thing in reality - it’s basically that probabilities correspond to how measures of the multiverse proportion themselves as differentiation occurs.
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
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
There is no contradiction. In Many Worlds Interprepation, Each World (and mostly importantly, with relative weight = 1, the World I am in right now) is built on probabilities.
Cache works on probability. Superscalar processor works on probability. L1, L2 ....cache works on probability
No mention of Metropolis-Hastings :(
It's the biggest, baddest, hammer in probabilistic machine learning.
It's the biggest, baddest, hammer in probabilistic machine learning.
Cool to see a conversation-style section
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
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
The book looks absolutely beautiful
From the preface: Is the result of a dice roll truly random or dependent on physics: angle, velocity, surface ?
Randomness is not absolute, but relative. For the one having the computer powerful enough to compute how the dice will roll and bounce, it is not random. For others, it is. That's why people with computers are not allowed into casinos.
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.
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.
I suggest acquainting yourself with quantum mechanics.
I suggest you do the same and learn that QM is not needed to compute movements of the dice roll, roulette or RNG computation.
An actual physical dice roll obeys QM, and if you want to compute how the dice will roll and bounce in the physical world, you’ll absolutely have to deal with QM, and true randomness will be involved.
It would be if you were looking for a perfect model of said die toss unless you are looking at it strictly from a purely theoretical and not actual physical die.
I believe in this scenario there are 2 different measures occurring. They do not seem to be playing a single dice roll, but many dice rolls. In that case you don't need a perfect simulation, but instead a good enough simulation to beat the house. Of course that's just more probability.
hmm probably
Probability theory works, with 100% chance even. Which annoyingly isn't the same as always.
The concept of probability is based on the concept of measure in math => limitation in its description of things, e.g., the probability for a real number in [0, 1) being an irrational number is 1.
Hold on, what measure over the unit interval assigns probability 1 to the set of irrational numbers in the unit interval? Do irrational numbers on their own even form a proper measurable set?
Lebesgue measure [0]. I never did write part 2 and many years have gone by with that blog languishing unmaintained on free wordpress but I wrote a thing that goes through the issues around this [1].
[0] https://en.m.wikipedia.org/wiki/Lebesgue_measure
[1] https://omnicognate.wordpress.com/2013/11/04/sigma-algebras-...
[0] https://en.m.wikipedia.org/wiki/Lebesgue_measure
[1] https://omnicognate.wordpress.com/2013/11/04/sigma-algebras-...
Of course. [0,1] has measure 1. Rationals have measure 0. Irrationals have measure 1-0=1
This question is why measure theory exists.
This question is why measure theory exists.
The irrationals are measurable for any measure that can measure points, which is most of them.
What is funny thought, that 0% chance events don't can't happen, but must happen. Like when you pick a point on a line, or roll a dice infinitely many times.
HMMs are probabilistic models, yes.
My Hypothesis: All matter exists in a sphere of probability. Our brains are masters of computing probabilities to tell us the most likely location for any object. It is not that we collapse the wave form, but that our brain ignores the wave form for our convenience.
Light is always a wave, never a particle. And a wave is just a probability.
Light is always a wave, never a particle. And a wave is just a probability.
Do you account for the fact that probability distributions can have multiple peaks with equal probability? If multiple brains were involved, they'd somehow have to coordinate on what they deem the most likely outcome.
Our brains all use the program, but we can see when some of these programs have a glitch. Take some LSD and you will see what I mean.
> 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?
> 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?
Say there is a quantum system – a particle or something – that has an equal probability to collapse in either of two classical states if measured. Say there are two scientists in a laboratory who perform a measurement on that system. If your hypothesis is true, how do they agree on what they perceive when looking at the result of the measurement? Each brain would have to make an arbitrary decision on which of the two equally likely outcomes to perceive.
How do all calculators know that 2+2=4?
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.
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.
Well, consider some of the political disagreements we've had in the last decade or so, we have ample evidence that two different people can look at the exact same thing and arrive at opposite conclusions.
Our brains would then exist in a state of probability too.
Yes, they do. But our minds do not. The brain creates the mind, the ego, and this is another collapse of a wave form.
so the brain creates the mind but it does not fully determine the mind?
why does the mind only experience one of the brains collapsed states?
why does the mind only experience one of the brains collapsed states?
The brain creates the function of the mind.
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”.
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”.
We need to connect - we are of the same mind. How do we do that? I have composed a 'book' on the topic and would love your thoughts.
awesome!
[email protected]
[email protected]
Hello again! I have tried to send you an email, but it says your address does not exist. I would very much like to connect!
Is the address correct, and I have made an error? Perhaps it's .net?
Thank you!
Is the address correct, and I have made an error? Perhaps it's .net?
Thank you!
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/