[HN Gopher] Probability (1963)
___________________________________________________________________
Probability (1963)
Author : rcshubhadeep
Score : 152 points
Date : 2022-10-10 08:46 UTC (14 hours ago)
(HTM) web link (www.feynmanlectures.caltech.edu)
(TXT) w3m dump (www.feynmanlectures.caltech.edu)
| sillysaurusx wrote:
| It's worth noting (much to my surprise) that the Feynman lectures
| on physics weren't written entirely by Feynman. I've often
| wondered whether the wonderful conversational style I've
| associated with him is actually him, or one of his
| contemporaries.
|
| Either way, this is a great chapter on probability. Thanks to
| whoever wrote it!
| mananaysiempre wrote:
| There's an unpleasant point in the history of the Feynman
| lectures: them coming out as "The Feynman Lectures on Physics
| by Feyman, Leighton, and Sands" is a compromise solution for a
| dispute where Leighton and Sands wanted to be credited for
| editing the transcript into readable prose and Feynman
| considered that work to be purely mechanical and not worth any
| credit at all[1]. (There is apparently more uncredited work in
| there as well[2].) "Feynman didn't understand editing is an
| art" is not much of a headline, but the compromise is still
| there, in huge letters right on the cover.
|
| [1] https://doi.org/10.1063/1.1955479
|
| [2] https://doi.org/10.1063/PT.6.3.20211209a
| barrenko wrote:
| Every great man is a Shakespeare.
| sillysaurusx wrote:
| I'll look terribly uncultured for asking this, but was
| Shakespeare a collection of individuals? That's very
| interesting; thanks.
|
| EDIT: Aha: https://en.m.wikipedia.org/wiki/Shakespeare_author
| ship_quest...
|
| Well, this is a fascinating rabbit hole. Apparently there's
| some question whether Shakespeare himself was literate, since
| his parents and daughters seemingly weren't.
| marcosdumay wrote:
| I guess the GP is more about the idea that Shakespeare was
| just the first one to write all the folkloric ideas of his
| time in a format that people loved, instead of that
| unexplainable genius that created all those interesting
| stories. (Kinda like Disney. But we don't have the
| originals anymore.)
|
| That one is a lot better accepted than the idea that he
| didn't write his works.
| bbarnett wrote:
| Shakespeare true or not, I have often found that when one
| excels, others sit on the sidelines, stupefied in
| disbelief, then shout cries of delusion about the accolades
| before them.
|
| Hence, Shakespeare cannot be real, for he excels you see...
| ageitgey wrote:
| Just keep in mind that the Shakespeare authorship
| conspiracy theory is the is the "the moon landing was fake"
| of the 1800s. The theory first gained popularly thanks to
| Delia Bacon in the 1850s, over 200 years after Shakespeare
| lived.
|
| There's no evidence Shakespeare didn't write his plays and
| a lot of evidence he did (including multiple books and
| writings published during this life listing him as author
| or referring to him as an author).
| darkerside wrote:
| Have you watched any of his videos? I don't know the exact
| style you're thinking of, but wonderful and conversational
| match what I've seen from him.
| stiff wrote:
| The "Feynman lectures on physics" books are based on actual
| lectures to Caltech students. You can listen to audio tapes of
| the lectures here:
|
| https://www.feynmanlectures.caltech.edu/flptapes.html
| sillysaurusx wrote:
| Thanks! Interestingly, the tape for Probability seems to be
| narrated by someone other than Feynman.
|
| I should probably give some evidence to back up my claim that
| Feynman didn't write all of the Lectures, but alas, it's
| late. I think the credits for the rest of the authors were in
| the preface, or at the end. I just wish they'd gotten a
| little more credit.
| stiff wrote:
| I think these people other than Feynman transcribed and
| edited the lectures into book form. This seems to have been
| the process with most (all?) books of his, "QED" and "The
| character of physical law" were also delivered as lectures
| and even "Surely You're Joking, Mr. Feynman!" was an
| interview originally that was later transcribed and edited.
| vmilner wrote:
| That someone is Matthew Sands:
|
| "Early on, though, a small problem surfaced. Feynman had a
| long-time commitment to be absent from Caltech the third
| week of the fall semester, and so would miss two class
| lectures. The problem was easily solved: I would substitute
| for him on those days. However, to avoid breaking the
| continuity of his presentation, I would give the two
| lectures on subsidiary topics that, although useful to the
| students, would not be related to his main line of
| development."
|
| https://physicstoday.scitation.org/doi/10.1063/1.1955479
|
| Later on he writes about the published books:
|
| "The next stumbling block was more serious: choosing a
| title for the book. Visiting Feynman in his office one day
| to discuss the subject, I proposed that we adopt a simple
| name like "Physics" or "Physics One" and suggested that the
| authors be Feynman, Leighton, and Sands. He didn't
| particularly like the suggested title and had a rather
| violent reaction to the proposed authors: "Why should your
| names be there? You were only doing the work of a
| stenographer!" I disagreed and pointed out that, without
| the efforts of Leighton and me, the lectures would never
| have come to be a book. The disagreement was not
| immediately resolved. I returned to the discussion some
| days later and we came up with a compromise: "The Feynman
| Lectures on Physics by Feynman, Leighton, and Sands."
| triknomeister wrote:
| That's horrible move from Feynman about credit.
| lupire wrote:
| It was also a "horrible" move for the two
| editor/publishers to claim equal author credit for
| Feynman's much more extensive creative effort.
|
| In reality, a simple negotiation led to a good decision
| that made everyone happy.
| vmilner wrote:
| [It's worth emphasising that Sands was hugely positive
| about the lectures and was great friends with Feynman.]
| wodenokoto wrote:
| If you scroll to the top there's a camera icon. If you click, you
| can view photos from the actual lecture
| graycat wrote:
| Sorry, Feynman, whatever else he did, on probability he gets a
| grade of flat F. Here is why: In his book _Lectures on Physics_
| he states that a particle of unknown location has a probability
| density uniform over all of space. No it doesn 't. No such
| density can exist. Done. Grade flat F.
|
| I tried to be a physics major but could not swallow all the daily
| really stupid mistakes such as this one by Feynman I got each
| physics lecture and I didn't have time both to learn the physics
| AND to clean up the sloppy math. So, I majored in math.
|
| As I learned the math, from some of the best sources, I came to
| understand just how just plain awful the math of the physics
| community is.
|
| Then in one of the Adams lectures on quantum mechanics at MIT I
| saw some of the reason: The physics community takes pride in
| doing junk math. They get by with it because they won't take the
| math seriously anyway, that is, they insist on experimental
| evidence. So, to them, the math can be just a heuristic, a hint
| for some guessing.
|
| Students need to be told this, in clear terms, early on.
|
| It went on this way: In one of the lectures from MIT a statement
| was that the wave functions were differentiable and also
| continuous. Of COURSE they are continuous -- every differentiable
| function is continuous.
|
| The lectures made a total mess out of correlation and
| independence. It looks like Adams does not understand the two or
| their difference clearly.
|
| There was more really sloppy stuff around Fourier theory. I got
| my Fourier theory from three of W. Rudin's books. It looks like
| at MIT they get Fourier theory from a comic book.
|
| I got sick, really sick, of the math in physics. Feynman on
| probability is just one example.
| jbay808 wrote:
| > a particle of unknown location has a probability density
| uniform over all of space. No it doesn't.
|
| In that case, in which locations is the density higher and in
| which is it lower?
| kgwgk wrote:
| > he states that a particle of unknown location has a
| probability density uniform over all of space. No it doesn't.
| No such density can exist.
|
| Not such a particle can exist then.
|
| You're assuming infinite space though. Did he?
| graycat wrote:
| Of course, the _space_ was not made explicit. With R the set
| of real numbers, the usual assumption in the physics is that
| the math is done in R^3 with the usual inner product, norm,
| metric, and topology.
| kgwgk wrote:
| The usual assumption in physics is that the observable
| universe is bounded.
|
| https://www.feynmanlectures.caltech.edu/I_05.html#Ch5-S6
|
| Edit: you may be talking about the paragraph "For an atom
| at rest," in
| https://www.feynmanlectures.caltech.edu/III_07.html#Ch7-S1
|
| The section starts saying that "We want now to talk a
| little bit about the behavior of probability amplitudes in
| time. [...] We are always in the difficulty that we can
| either treat something in a logically rigorous but quite
| abstract way, or we can do something which is not at all
| rigorous but which gives us some idea of a real situation--
| postponing until later a more careful treatment. With
| regard to energy dependence, we are going to take the
| second course. We will make a number of statements. We will
| not try to be rigorous--but will just be telling you things
| that have been found out, to give you some feeling for the
| behavior of amplitudes as a function of time. "
| graycat wrote:
| I put in a qualification:
|
| > ... the usual assumption in the physics is that the
| math ...
|
| Soooo, you got into the physics. I avoided getting into
| the physics. E.g., when Newton wrote out his second law
| or Maxwell wrote out his equations, it was just _math_
| and the assumption was as I mentioned R^3. Stokes
| theorem, the Navier-Stokes equations were implicitly in
| R^3.
| kgwgk wrote:
| > Soooo, you got into the physics. I avoided getting into
| the physics.
|
| What did you think that Feynman's Lectures on Physics
| were about?
| Gatsky wrote:
| You rage-quit physics, essentially.
| mturmon wrote:
| It's tough.
|
| I used to work in an area of applied probability where some
| statistical-mechanics principles were applicable. I'd read
| papers where authors were making analogies of a large neural
| network to a stat-mech system, using an applicable stat-mech
| approximation, and then differentiating that approximation to
| get a probability bound.
|
| It gave interesting results, and did show you something about
| the original problem that was hard to get by sticking to the
| original formalism. But at the end of the day, you really would
| not bet the farm on the truth of those approximations...
|
| On the other hand, Fourier analysis was originally doubted and
| scorned by mathematics, but (if I'm remembering the story
| correctly) ended up being used so much that theory was
| developed to explain in what sense the Fourier transform
| approximates the original function.
|
| Another example of the interplay between physics and
| mathematics is the percolation problem, where there was a kind
| of archipelago of physics-motivated results that probabilists
| have been trying to tidy up for decades now. E.g., sec. 1.2 of:
| https://www.unige.ch/~duminil/publi/2018ICM.pdf
| q-big wrote:
| > Sorry, Feynman, whatever else he did, on probability he gets
| a grade of flat F. Here is why: In his book Lectures on Physics
| he states that a particle of unknown location has a probability
| density uniform over all of space. No it doesn't. No such
| density can exist. Done. Grade flat F.
|
| I would rather consider that because it seems that you "need" a
| uniform distribution for a particle of unknown location, it
| might makes sense for such applications from physics to weaken
| the property that a probability measure has to be s-additive to
| that a probability measure has to be additive. Then it should
| be possible to define such a "uniform probability 'measure'
| over all space", perhaps similarly to the example given at
|
| > https://en.wikipedia.org/w/index.php?title=Sigma-
| additive_se...
| hither_shores wrote:
| > really stupid mistakes such as this one by Feynman
|
| It's not a mistake, it's a "lie-to-children" fundamentally no
| different from an intro analysis class talking about "the" real
| numbers. Freshmen aren't ready for model theory, and they're
| not ready for rigged Hilbert spaces.
| dchftcs wrote:
| >probability density uniform over all of space
|
| If space is bounded then such a density can exist.
| clircle wrote:
| What is the problem with density on space?
| graycat wrote:
| Take one cubic inch. Let the probability the particle is in
| that cubic inch be p. Then take integer
|
| n >= 2 / p
|
| cubic inches. Then the probability that the particle is in
| those n cubic inches is
|
| np >= 2 > 1
|
| greater than 1, a contradiction. Done.
|
| One well considered and informed explanation is that the
| physics community abuses its students.
| clircle wrote:
| There's no uniform distribution on an infinite space...
| hackandthink wrote:
| Probability Theory without Measure Theory is advancing.
| Interestingly Tobias Fritz is a Physicist.
|
| "A synthetic approach to Markov kernels..."
|
| https://arxiv.org/abs/1908.07021
| dchftcs wrote:
| graycat's pedantic approach to mathematical formalism is
| quite defeatist in that it basically disallows any
| mathematical concept to advance from precise but limited
| language towards the edge of imagination. The kind that
| forbids sqrt(2) from existing in the Pythagorean days.
|
| A probability theory that accommodates the concept of
| "picking a random even number from all integers" can be
| valuable, isn't compatible with measure theory but is
| easy to grasp intuitively. When the mathematical tools
| aren't good enough you still want to be able to reason
| about concepts, which is why the tools are developed to
| begin with. Fortunately almost all things are
| conceptually tractable when dealing with finite space or
| quantities; if a statement can be transformed to
| something rigorous (if numerically imprecise) by forcing
| boundedness it's not too terrible to speak in unbounded
| terms when the physical world is what you want to model.
| I can understand why physicists don't want to be burdened
| with too much about rigor - they can afford the small
| risk they're wrong sometimes, but can't afford to slow
| down their search for new discoveries, when so many
| questions remain unanswered.
| vitus wrote:
| One counterargument is that space is finite, and so your
| choice of n is greater than the volume of the universe.
| (And so sigma-additivity doesn't apply, since your choices
| of cubic inches are not disjoint.)
|
| But sure, if you're assuming an unbounded space with finite
| measure, a uniform density across that space must be
| identically zero everywhere.
| graycat wrote:
| > identically zero everywhere.
|
| Not a probability density.
| sylware wrote:
| What's astonishing: many laws of physics emerge from statistical
| approximations of quantum mechanics.
|
| One day, if I really get into quantum mechanics, I will try to
| understand how they rebuilt maxwell equations from QED.
| ThomPete wrote:
| Not if you submit to the Everett interpretation.
| marginalia_nu wrote:
| Classical behavior emerges from quantum mechanics as you enter
| the classical domain.
|
| This can be explained through phase decoherence. As temperature
| rises, random phase shifts are introduced, which effectively
| removes the quantum effect. You can show mathematically how
| this works.
|
| Consider the young experiment:
|
| https://imgur.com/FqogDJj
|
| For a plane wave ps ~ e^(ipx/h-iot), the wave function at X is
| the sum of two components
|
| <X|ps> = <X|P> + <X|Q>
|
| Where for some path-independent normalization function ps(X,t),
| and using the small angle assumption (QX-PX = 2Xa/L), the
| components are: 1 ipXa/hL
| <X|P>= ps(X,t)- e 2
| 1 -ipXa/hL <X|Q>= ps(X,t) - e 2
|
| And the probability of finding the particle at X is
| 2 2 2 pXa |<X|ps>| = |ps(X,t)| cos -----
| hL
|
| That is what you'd expect from the Young experiment. If we
| introduce a constant phase shift ph between P and Q, you get
| this average instead: 2 2 2
| pXa |<X|ps>| = |ps(X,t)| cos (--- + ph)
| hL
|
| If this phase shift is instead random, the formula becomes
| 2 1 ^ pXa 2 |<X|ps>| -
| (1 + | dph P(ph)cos(2 --- + 2ph)) |ps(X,t)| 2
| v hL
|
| Where P(ph) is a probability function for the phase shift. If
| the probability function is flat, the integral is zero since
| you're integrating the cosine across its domain. What you get
| is the classical result! 2 2
| |<X|ps>| = |ps(X,t)|
|
| You can even re-phrase random phase shifts into a diffusion
| equation, and find that given a as the diffusion coefficient
| 2 2 1 -at 2 pXa |<X|ps>| = |ps(X,t)| -
| (1 + e cos (--- + ph) ) 2
| hL
|
| i.e. the transition behavior from quantum to classical
| dependent on a direct measure of the decoherence!
|
| a small => quantum result, a = large, classical result.
| UniverseHacker wrote:
| How did you typeset all of that math into hn?
| marginalia_nu wrote:
| Painstakingly.
| mhh__ wrote:
| Read Quantum field theory for the gifted amateur
| programmer_dude wrote:
| I think you mean "ab initio".
| killjoywashere wrote:
| QED = Quantum electrodynamics, for which Feynman won the
| Nobel Prize.
| sylware wrote:
| Yeah, I meant the latest QED based on the lastest QFT.
| programmer_dude wrote:
| My bad.
| mfn wrote:
| Regarding how to derive Maxwell's equations from QED, I'd
| recommend this lecture:
| https://theoreticalminimum.com/courses/special-relativity-an...
|
| This derivation is in the context of classical field theory,
| but QED is only a short hop away through path integrals.
|
| It's quite remarkable how the complexity of Maxwell's equations
| can be reduced to a single term in the Lagrangian -
| (F_uv)(F^uv), assuming no charges. That's really it!
| hackandthink wrote:
| Everybody knows Feynman, who knows Jaynes?
|
| https://quantumfrontiers.com/2018/12/23/chasing-ed-jayness-g...
|
| Jaynes about Probability in Science:
|
| https://www.cambridge.org/gb/academic/subjects/physics/theor...
| mananaysiempre wrote:
| Jaynes is brilliant, but you ought to take care when reading
| him. For example, AFAICT his digression on Godel's theorem in
| _Logic of science_ is complete nonsense, and the rant against
| Kolmogorov-style axiomatization of infinite probability spaces
| in same isn't much better.
| kgwgk wrote:
| "From many years of experience with its applications in
| hundreds of real problems, our views on the foundations of
| probability theory have evolved into something quite complex,
| which cannot be described in any such simplistic terms as
| 'pro-this' or 'anti-that'. For example, our system of
| probability could hardly be more different from that of
| Kolmogorov, in style, philosophy, and purpose. What we
| consider to be fully half of probability theory as it is
| needed in current applications - the principles for assigning
| probabilities by logical analysis of incomplete information -
| is not present at all in the Kolmogorov system.
|
| "Yet, when all is said and done, we find ourselves, to our
| own surprise, in agreement with Kolmogorov and in
| disagreement with his critics, on nearly all technical
| issues. As noted in Appendix A, each of his axioms turns out
| to be, for all practical purposes, derivable from the Polya-
| Cox desiderata of rationality and consistency. In short, we
| regard our system of probability as not contradicting
| Kolmogorov's; but rather seeking a deeper logical foundation
| that permits its extension in the directions that are needed
| for modern applications."
| hackandthink wrote:
| I've read in Quantum Information Theory papers, that Jaynes
| misunderstood Bell (he just didn't get it).
|
| https://physics.stackexchange.com/questions/233203/has-
| jayne...
| kgwgk wrote:
| I just found this recent writeup on the subject, I didn't
| have time to read it yet but looks interesting (he hasn't
| been active on HN for almost two years, by the way).
|
| https://scottlocklin.wordpress.com/2022/06/06/poking-
| holes-i...
| vmilner wrote:
| Well, I do... :-)
|
| Less facetiously, I think Jaynes is becoming better known as
| Bayesian techniques have become more mainstream.
| UniverseHacker wrote:
| "rationalists" are obsessed with Jaynes, in as much as HN
| overlaps with that community I'd say a lot of people on here
| are familiar
| jqgatsby wrote:
| The best study guide to Jaynes that I've found is from David
| Blower (sadly, recently deceased):
|
| Information Processing: The Maximum Entropy Principle
| https://a.co/d/71tL5bw
|
| He really takes apart the maximum entropy principle in a
| comprehensible way, to the point where one can see how to apply
| it to new problems.
|
| (the volumes I and III are also good but not strictly
| necessary)
| hackandthink wrote:
| A simple example by Nassim Taleb:
|
| https://www.fooledbyrandomness.com/blog/2021/09/07/estimatin.
| ..
| akuro wrote:
| Anybody who loves statistical mechanics has surely heard of
| Jaynes.
|
| Unfortunately, those who like statistical mechanics seem few
| and far between. :(
| code_biologist wrote:
| Reminds me of a classic quote from a stat mech textbook:
|
| "Ludwig Boltzmann, who spent much of his life studying
| statistical mechanics, died in 1906, by his own hand. Paul
| Ehrenfest, carrying on the work, died similarly in 1933. Now
| it is our turn to study statistical mechanics."
|
| David L. Goodstein, States of Matter
| B1FF_PSUVM wrote:
| Well, who likes having it pointed out that all the air in the
| room huddling in a corner is a possibility, albeit very, very
| small ...
| deltasevennine wrote:
| I have a related question to this topic. Is probability axiomatic
| to reality? Does it exist on the same level as logic where logic
| is axiomatic to reality and just assumed to be true? Or is it
| simply a phenomenon arising from logic?
|
| It seems like probability just happens to work without
| explanation? Intuitively this seems a bit strange since it feels
| as though probability should be derived from something else. Not
| sure if I'm correct here.
|
| What confuses me even more is that I do know logic can be defined
| in terms of probability. Causal connections can be probabilistic.
| If A then 25% chance of B and so on.
| quickthrower2 wrote:
| A lot of what probability is, is the extent of lack of
| information.
|
| The Monty Hall Problem is a great example of this.
|
| So I would say the more fundamental thing might be information
| theory.
|
| This my layman view. Not an expert.
| lupire wrote:
| Probability is weight/count of cases of interest divided by
| weight/count of all possible cases.
| quickthrower2 wrote:
| I just rolled a 6 sided die here and looked at the outcome.
| For you the probability it is a 6 is 1/6. For me is isn't
| 1/6. Same object!
| mturmon wrote:
| Perhaps you're just kidding around, but of course that's
| not good enough for a definition.
|
| It doesn't handle continuous random quantities. It doesn't
| even handle situations with a discrete outcome but where
| counting the possible cases isn't well-defined (Buffon's
| needle being one, but an even better one being the chance
| of a tossed thumbtack landing point-up). It also doesn't
| handle cases where symmetry or physics can give the answer,
| but you can't count cases because they aren't finite or
| aren't necessarily a-priori equiprobable.
| nyc111 wrote:
| Probability, seems to me, cannot be fundamental, because, a
| machine built to flip a coin with always the same pressure, can
| be adjusted to always give heads, or tails. In such a setup
| there won't be probability.
|
| From George Boole's The Laws of Thought, p.244: "Probability is
| expectation founded upon partial knowledge. A perfect
| acquaintance with _all_ the circumstances affecting the
| occurence of an event would change expectation into certainty,
| and leave neither room nor demand for a theory of
| probabilities."
|
| Can we deduce from this that nature is not probabilistic?
| dariosalvi78 wrote:
| unfortunately nature IS, most likely, probabilistic:
| https://en.wikipedia.org/wiki/Hidden-variable_theory
| likeabbas wrote:
| What if the machine was built with 99% precision?
| notafraudster wrote:
| It is true that (at least above the level of quantum physics)
| we tend to believe that reality is deterministic. When the
| meteorologist gives a chance of rain, in truth if they had
| perfect forward information on all of the clouds and pressure
| systems, they would simply declare whether or not there was
| future rain. In cases like physical phenomenon, you can think
| of observed uncertainty or chance as being a product of the
| exact settings of the unmodeled but deterministic factors
| underlying a particular outcome, or else errors in the
| functional form of the model with respect to the measure. We
| tend to assume that unmodeled factors are as-if orthogonal to
| the causes we are interested in modelling, and thus zero-
| centered, and our models minimize error predicated on this
| assumption.
|
| In your proposed flipping model, there are likely to be very
| small physical imprecisions (vibrations in the flipper, say,
| drifting tension of some kind of spring or actuator, or small
| amounts of circulating air, or perhaps tiny imprecisions in
| the way the coin is loaded into a slot). The machine might
| always flip heads, but it's still possible to say that
| whatever arbitrary degree of certainty you need to model the
| coin's behaviour in the air to achieve 100% accuracy, there
| could still be arbitrarily smaller error below that
| threshold, and we'd view this as "randomness" even if it
| isn't by the laws of physics.
| empyrrhicist wrote:
| Not a physicist, but your argument is pretty unconvincing in
| that it relies entirely on intuition about classical physics,
| ignoring quantum phenomena entirely. If one were to argue
| that probability were fundamental, they'd very likely start
| by describing wave functions, which are probabilistic and
| seem pretty close to fundamental to observable reality.
| kqr wrote:
| There are two things we mean by "probability". The first is
| propensity, and this has clear links to information theory, as
| another person commented about already.
|
| It's important to emphasise that in terms of propensity, it
| doesn't matter whether or not the event has occurred, what
| matters is your knowledge about it. A flipped fair coin has a
| definite side up (as can be verified by a silent third
| observer) but for you, who has not yet observed which side it
| is, your best guess is still either side with 50 % probability.
|
| Similarly, if you only know there's a soccer game going on, you
| might guess that the stronger team will win with 60 %
| probability (based on historic frequencies of exchangeable
| situations), but someone who has seen the score and knows the
| weaker team has a lead and knows there's only a few minutes
| left of the game will judge there to be a 2 % probability the
| stronger team wins. Same situation, different information,
| different judgements.
|
| That's the first meaning of "probability". What we also mean
| with that word is "the rules of probabilistic calculation".
| These are based on mathematical ideas like coherency (if one of
| two things can happen, their probabilities should add up to 100
| %) and can definitely be taken as axiomatic.
|
| All of this is not an answer to your question, but it might
| make the discussion richer.
| kgwgk wrote:
| There are multiple interpretations (corresponding to your
| first part). One of them is indeed about "propensities" but
| the most common ones are about "frequencies" and about
| "uncertainty".
| panda-giddiness wrote:
| Probability theory can be interpreted as an extension to logic
| where variables can take fractional values (rather than just be
| 0/false or 1/true).
|
| E.g., ((A or B) and C) = (A and C) or (B and C)
| => P[(A or B) and C] = P[(A and C) or (B and C)] =
| P[(A and C)] + P[(B and C)] - P[(A and B) and (A and C)]
| = P[(A and C)] + P[(B and C)] - P[A and B and C] =
| P[A|C] P[C] + P[B|C] P[C] - P[A and B and C]
|
| Notice the last couple lines -- this is the way in which
| probability extends logic. In you take the limit where P[A],
| P[B], P[C] = 0, 1, then the probability statement reduces to
| the logic statement at the top.
| BOOSTERHIDROGEN wrote:
| Also in relation to reductionism.
| ThomPete wrote:
| Probability does not exist in reality as it's open ended. It
| does however exist in ex a deck of cards and a game that's
| defined.
|
| Probability is often being misused to say things about reality
| though. You see that especially in computer simulation whether
| used in economics, weather etc.
|
| Different initial conditions are put into the models and
| simulated. And the probability is calculated based on what the
| majority of those models say.
|
| But those initial conditions are guesses not actual objective
| explanations. If they were you only needed to run one
| simulation rather than a range.
|
| A lot of statistics is pure placebo. Purely retrospective.
|
| In reality it either is or it isn't. If you have good
| explanations like we do in physics you don't need probability.
|
| David Deutsch IMO has the most sane rebuttal of the
| probability.
|
| http://www.daviddeutsch.org.uk/2014/08/simple-refutation-of-...
| fjkdlsjflkds wrote:
| > In reality it either is or it isn't. If you have good
| explanations like we do *in physics you don't need
| probability*.
|
| So... are you saying Statistical Mechanics (to give an
| example) is not part of Physics?
|
| In real life, the amount of information you have (and _can
| have_ ) about a physical process is limited. You can either
| throw your hands up and say "we can't know for sure", or you
| can use probabilities to try to get somewhere.
|
| How do you define the position of an electron without using
| probabilities?
| ThomPete wrote:
| Just because it's limited doesn't mean I can assign
| probability to it.
|
| As I said. The difference is closed and open systems.
|
| No problem with probability of getting a given card based
| on what have already been dealt in ex a game.
|
| The problem arises when it's applied to predicting reality
| in open ended systems as I said weather, economics, climate
| etc. and where history is being used as some sort of
| benchmark of the future.
|
| There is no probability whether an astroid is on the path
| towards earth. It either is or it isn't.
|
| In other words. We can either explain or not.
| fjkdlsjflkds wrote:
| So, would you claim that: "There is no probability
| whether an *electron* is on the path towards earth. It
| either is or it isn't."? I guess you must know something
| that Heisenberg didn't.
|
| Good luck defining things such as "path" and "position",
| without using probabilities, for non-macroscopic objects.
|
| Also, what is your opinion about the classical "double-
| slit experiment"? Either a particle passes through a
| slit, or it passes though the other, right?
| kgwgk wrote:
| There is no probability whether the next card in the deck
| is an ace. It either is or it isn't.
| ThomPete wrote:
| There is a probability, it can be described based on what
| cards have already been dealt. It does not change whether
| that specific card is an ace or not.
|
| So yes we agree.
| kgwgk wrote:
| Do we also agree that - even if you don't - other people
| are able to conceive a probability that the next card in
| the deck is an ace, a probability that I was born on a
| Saturday, a probability that Germany wins the World Cup,
| etc.?
| ThomPete wrote:
| It's not the discussion whether people can conceive all
| sorts of things. The discussion is about its relationship
| to reality.
| kgwgk wrote:
| I'm pretty sure you can as well!
|
| If you can pick Brazil or Morocco to win $1000 in case
| the one you choose wins the World Cup which one do you
| pick? Why?
|
| Are you really indifferent between them because you
| cannot conceive how saying that one is more likely to win
| than the other could have any relationship to reality?
| kqr wrote:
| > In reality it either is or it isn't. If you have good
| explanations like we do in physics you don't need
| probability.
|
| You mean good explanations _and_ observations? You 're
| absolutely right in that if you are able to observe all the
| relevant information with no noise, you don't need
| probability. But there are a lot of systems where you can't
| noiselessly observe what you want - this is where probability
| is important.
| ThomPete wrote:
| Yes probability have its place for ex error correction in
| closed systems.
|
| But you can't predict the future with it. That's what I am
| trying to get at.
| kqr wrote:
| So what general method of predicting the future are you
| using that's better?
|
| Try to avoid the opt-out "I don't predict the future
| unless I have perfect explanations of everything" because
| I know you don't -- no-one does.
| ThomPete wrote:
| I use the same one as you. I conjecture based on my
| ability to explain why I think x will happen or wont
| happen.
|
| No amount of putting percentages on X changes X. It
| either happens or doesn't.
| kqr wrote:
| So if I asked you whether you found it more likely that
| you'll ride a helicopter tomorrow, or that a Democrat
| will be elected president in the next US presidential
| election, what would be your answer and why?
| ThomPete wrote:
| I would say "I don't know" and I would be lying if I said
| anything else.
|
| I can tell you I don't have any plans of going on a
| helicopter ride tomorrow. I can also tell you that I have
| no idea if the next president will be democrat.
|
| What formula do you propose we use to calculate the
| probability?
| kqr wrote:
| And if I proposed a bet where you pay me $10 now and I
| pay you $40 if there's a Democrat president next
| election, you wouldn't take the bet because "you don't
| know?"
|
| (This situation could be put in a less abstract way:
| there's a business opportunity that costs some money to
| realise but you only reap the benefit in the right
| political climate.)
| ThomPete wrote:
| I might take the bet but I would just be guessing or I
| might work towards trying to find a solution to turn the
| guess into an explanation.
|
| At no time does probability help me with figuring out
| what the outcome is.
|
| I can either explain what will happen or I can't. There
| is no 50/50. I just don't have the correct explanation
| i.e. an explanation that is hard to vary.
| kqr wrote:
| Can I interpret your taking the bet as an admission that
| it's a bet that comes with a positive expectation? (In
| the sense that if you took similar bets very many times,
| you would end up with an almost sure profit.)
| kgwgk wrote:
| > If you have good explanations like we do in physics you
| don't need probability.
|
| Who is we? A lot of physics textbooks have a good amount of
| probability at their core.
| ThomPete wrote:
| Yes and most of that is wrong. Physics doesn't deal with
| probability but with explanations. (Yes also in QM)
| [deleted]
| kgwgk wrote:
| Explain that to the Royal Swedish Academy of Sciences.
| Maybe they can still take back this year's prize and give
| it to some physicists who deserve it.
| mturmon wrote:
| That David Deutsch web-link is not saying what you think it's
| saying.
| BOOSTERHIDROGEN wrote:
| Any statistics book that have similar approach like this ?
| kqr wrote:
| This was much more common in the first 2/3 of the 20th century
| than it is today. I can strongly recommend _Theory of
| Probability_ (de Finetti, compiled 1970 based on work de
| Finetti did as early as 1930s) and _Foundations of Statistics_
| (Savage, 1972) - the latter leans a bit on the former but
| expands on it with useful perspectives.
|
| I recommend you start with these basic theoretical books to get
| a sense of what it's all built on. But then if you want more
| practical advice about how to handle things, books on sampling
| theory tend to hit a sweetspot between theory and practise, in
| my experience. I like _Sampling Techniques_ (Cochran, 1953) and
| _Sampling of Populations_ (Levy & Lemeshow, 2013).
| BOOSTERHIDROGEN wrote:
| Thanks for the sampling techniques.
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