When I was studying quantum mechanics, I quite often went to this book for a very different perspective on a lot of the details. I found it to be exceptionally well written and had a seemingly different approach from the typical college or graduate level quantum mechanics textbook. We had a copy in one of our department libraries, if you can get your hands on one, I recommend giving it a read when you want a new perspective on an academic quantum mechanics concept :)
I am far enough away from that part of my life, I apologize for not being able to give a more detailed and convincing testimonial for this book.
Indeed. Not only can one get a glance of a unique perspective of one of the founding fathers, but also a lot of important facts not covered in many other textbooks. One of such facts are the low heat capacities of atoms that do not fit any classical theory. This fact alone is able to kill most of the "alternative" interpretations of quantum mechanics that the popular media sell-off as "science" nowadays.
My impression of the different quantum mechanics interpretations (copenhagen, many worlds...) is that they are observationally equivalent. Is this not true?
In modern times, the Y combinator has been made famous by the Y Combinator startup accelerator, named that way by Paul Graham (who had been a longtime enthusiast of functional programming and the LISP programming language—and had written an early web store using it) because (as he once told me) “nobody understands the Y combinator”. (Needless to say, Y Combinator is all about avoiding having companies go to fixed points…)
If you're in London and in any way interested in computing history, you owe it to yourself to visit Bletchley Park. It's a fantastic day visit from London. (About an hour away or so via the railway, as I remember it.)
There's a direct train from Paddington, iirc. UK people please fill in.
An on-site museum of the WW2 Enigma code breaking activities, where they happened. This is where Alan Turing worked. Live demonstrations of the 1940s eras computer "bombes".
But, perhaps, most of all:
A chance to visit a historic site.. the activities there could very well have decided the outcome of WW2.
There's also a neat live retrocomputing display of early home computers. And it also happens to be a very lovely area to hang around in - nice buildings, park areas, ponds etc.
Well, you can see an original Enigma machine at Churchill's war room, with a nice quiz about the facts that the allies pretended they didn't know about. The Science Museum also has nice displays about Alan Turing work. Some time ago they hosted the exposition Code Breaker: https://www.sciencemuseum.org.uk/what-was-on/codebreaker
The Science museum is a sad picture of extreme neglect and bad ideas these days. Just about every museum I've been to in the UK does it better, whether regional ones or national, even the smaller ones. Manchester Museum of Science and Industry, Bletcheley, Royal Arms Leeds, etc.
Bletcheley has a far, far better discussion about Turing and his influence, and far better displays of the Code Breaking work, along with the associated machines.
I last went to the Science Museum about 5 years ago and all the precision models were gone - some of which were so clever and detailed they should have been exhibits in their own right. Just a couple of hints that they once had extreme skill in model making are left. A good chunk of the multimedia and electronic displays and "experiences" were dysfunctional in some way, and a lot of the classic topics had exhibits that appeared simply worn out. The basement "scientific art exhibition" was about 5 token exhibits in a space the size of a football field, and a few dozen people finding somewhere quiet to sit and eat their sandwiches. The top floor (I think) was the for children interactive, sponsored experience. More was broken than not. The cafe with eye-watering prices seemed the most recent and best maintained exhibit.
I was so disappointed - so were the people we took, for whose benefit we made the trip at all. Manchester MSI is far better at being a science museum nowadays. Have to start to wonder if my extreme love of the place in the 60s-90s stems as much from nostalgia and rose-tinted specs. It's deeply sad, and should be criminal, that it's been allowed to decline that far - it was once a world renowned national asset.
I agree that many parts of the Science Museum now look neglected and shabby, but the museum does have some truly exceptional exhibits - an original prototype Analytical Engine, a working replica Difference Engine, an Apple I, a Cray 1a, a Daniels Space Traveler and much more besides.
I have to admit a deep sadness at the recent closure of the old Wellcome collection on the fourth and fifth floor; this gallery had been left largely unchanged in several decades, but it had a powerfully evocative atmosphere. It was nearly always empty (hence the understandable decision to close it) and was poorly signposted from the rest of the museum, so it felt almost like urban exploration, creeping through a once-cherished but now abandoned site. By the passage of time, it had become a sort of meta-museum, presenting a historical perspective on the history of medicine. The galleries have been preserved for posterity by Google, but pictures can't really capture the feeling of stepping into a museum that is itself a museum exhibit.
I think so much of it reflects its decades as increasingly underfunded state asset, in an era when having a state asset at all is almost unacceptable.
I imagine budget for proper replacement displays, modelling, maintenance and restoration is far harder than it used to be... Some of those exceptionals, both known and lesser known in storage, deserve far more than they now often get.
> recent closure of the old Wellcome collection ... powerfully evocative atmosphere
Ugh. That hard to define atmosphere is the part that seems to being modernised away, and a good part of what I increasingly miss. Whether it's too many "clean" experiences with acres of empty space and a few exhibits spotted around, or the changing nature of the interactive models I'm not sure. Certainly I think a lot of the screen based stuff would be better as interactive experience on the website than in the building, though when it's additional to other means, it can often work.
I wish a lot more of how they managed was additive rather than replacing great swathes with a whole new design. Most, though not all, of the new plastic and electronic approaches seem far poorer in terms of lasting, and often less engaging.
The parts I often enjoy most are the esoteric, failed but promising ideas, and the day-to-day that we forgot. So I like the odd little packed displays of thirties electricals, analogue computers,
> By the passage of time, it had become a sort of meta-museum
This is one unexplored area they could do so much more with. Beautiful teak and brass cabinets with a perfect cutaway replica of a steam turbine or whole power station might not be the modern way to do it, but they were lasting and beautiful of themselves. 8 or 10 year old me couldn't leave the place until I'd turned every handle. :)
I'm sure there's scope for a huge, and fascinating self-referential meta-museum of presenting museum science, model making and all the other back room activities through the ages. Include some of the long forgotten exhibits that included the scent of machine oil, carbon electrical brushes, the metallic bite of a little ozone and sprinkling of burnt dust - like all machinery used to come with. Oh, and a selection of those ancient models the kids can try, and fail, to break by winding too fast.
Maybe we need a museum of the museum - maybe that's V&A's territory. :)
I just hope that now Manchester Science and Industry are under the same group it brings the London Science Museum up, rather than Manchester down.
SW has a tendency to describe features of a person which I find utterly fascinating (for eg: 'Turing used to giggle a lot', now compare that with the somber depiction of Turing in 'The Imitation Game'). In the write up on Ramanujam, SW mentions that he was stocky, apart from many personal tidbits.
"Bullying by the state" is not a conspiracy theory. He was actually, objectively punished by the state in a manner that is considered cruel and inhumane by modern standards.
The sentence is a train wreck to begin with. "Conspiracy theory" isn't a potential cause of death, and these things do not really form a coherent range. Presumably the conspiracy theories allege murder? In that case, I might write something like: "Turing's death is still an openly debated topic, with purported causes of death including simple accident, suicide resulting from bullying by the state, and even murder at the hands of a conspiracy."
If you follow the link to the obituary for Nicholas Kermack in the Eton Chronicle, then turn to the next page, you will see that at the time it was edited by Roger Clarke, who went on to be a film reviewer for The Independent, and also someone called Boris Johnson.
He mentioned that Cambridge switched to four digit phone numbers in 1939. Where can one find out such things like that, where did they record and document it as a fact? I wonder if they still had manual operators or was that automatic switching?
the link: [1] the first automatic switch was introduced in 1922; so they had the fascinating problem of interoperation between manual switched regions and automatic ones. So that Oxford might have had it either way.
I’m not an expert on the topic at all, but the story always seemed fishy to me. Who kills themself by injecting an apple with poison and eating an apple?
(The JFK story also seems fishy to me because I don’t get why in the world Jack Ruby killed Oswald)
Ruby was under the delusion that the world would forgive him for it because everyone hated Oswald so much for having offed JFK. And, that he would be labeled a national hero.
There's some doubt. He did electroplating as a hobby for which he used potassium cyanide. He could have inhaled hydrogen cyanide fumes, or not washed his hands well enough before eating the apple. So it might have been accidental death.
Having worked with similar chemicals, you tend not to get careless. I would wager a majority of cyanide injestions are not accidental. I think murder or suicide is much more likely, particularlly given the context.
A real shame that Wolfram gives credence to "handwriting analysis" pseudoscience in what is otherwise an interesting piece.
> “The writing style is entirely different. Personality-wise, the writer of sample B has a quicker, more intuitive thinking style than the one of sample A.”
How can anybody of Wolfram's intelligence unquestioningly accept this nonsense?
Because handwriting analysts tell people they are an accepted branch of psychology and there is not enough time in the day to question everything. At some point, I heard handwriting analysis was pseudoscience, so I looked into it and they were right. I've not looked into whether quantum physics is pseudoscience because the people in my life who appear to be experts in the subject tell me it's real and I don't feel like pursuing a physics degree to tell if they're full of it. Regardless of the perception you have of yourself as a critical thinker, for most things we accept thinds as true by default and only flag certain suspicious things for further criticism.
Your assertion that Wolfram "unquestioningly accepted this nonsense" is unfounded.
Ignore the personality assessment element. Wolfram sought to identify whose handwriting the note was, so he asked a "professional handwriting examiner" that he happened to know. The quote you extracted was her relaying her opinion that the note was not written by Turing.
Equally interesting - have you read the research that (dis)credits handwriting analysis, or you just unquestionably accept that it's nonsense?
Similar to other personality-related pseudopseudosciences, there's enough contradicting research to form any opinion (or, more commonly, to support your pre-existing one) [1] [2].
I think the popularity of this method is mainly the result of Forer effect [0]
I write a lot. I can tell from my own experience that what I'm feeling when I write translates into my handwriting in subtle ways. You may object to some particular method that I'm unaware of, but I don't think "handwriting analysis" in general is absurd. It's data and so there are models of it and inferences.
Personal feelings are not how we evaluate a scientific discipline. It's phrenology level nonsense.
A coworker once told me that his chiropractor told him he could help him with hemroids. This not only made me dubious about her ability to cure hemroids. It made me dubious that she could do anything about back pain. Capable people don't spew nonsense within the scope of their capabilities.
The second his analyst registered an opinion about the personality of the writer I became dubious that she could even tell who wrote it.
People felt the same way about Einstein's cosmic intuition. Things evolve in stages, from intuition and anecdotes to more formal developments or refutations. I didn't say handwriting analysis is a fully legitimate area. I said as a writer I see how my writing changes and don't find the concept as absurd as many here do because of my anecdotal experience. You may hand wave that away because I don't have a statistical analysis here that is peer reviewed, and that's fine, but to me saying something is nonsense without a proof that it's nonsense is equally bad. Everything that isn't completely rigorous isn't nonsense. It's not good science, but not necessarily nonsense.
It’s not outside the realm of plausibility that certain chiropractic procedures could help with digestive issues linked to other issues. There’s been a decent amount of research recently into stimulating the vagus nerve for example and how it affects not only digestion but also mood and immune function. If a pinched spinal nerve is causing digestive issues perhaps it could lead to other issues. Curing every case? Likely not, but perhaps it could help some individuals. Now the chiropractic field is also full of half baked practitioners as well, imho.
I know SW is famous for his arrogance/egotism, but it still kills me how he always discusses everything in terms of Mathematica's programming language, instead of mathematical notation or pseudo-code. It's like giving a linguistics lecture using the made-up language you invented with your twin.
I don't think your criticism is very accurate here. Wolfram Language code doesn't show up until the second half of the (very long) article, in the sections where he is explaining how to represent the mathematical concepts in the Wolfram Language. In fact, in several cases he mentions the traditional mathematical notation and follows it with the Wolfram Language notation. What's strange or arrogant or egotistical about this? Yes, he's the founder and CEO of the company that created the language, but that doesn't strike me as a problem. It's a good language for doing this sort of thing, and it's pretty clear that he's genuinely interested in both the mathematical concepts and how to create a programming language to represent them. This is hardly just content marketing blogspam.
Every single piece Wolfram writes, without exception, is arrogant content marketing blogspam. Even his books. Sometimes very clever, sometimes interesting (though I'd find him 1,000x more interesting if say 1 article in 10 made no mention of how clever he and Mathematica are); always arrogant and self-promotional. This piece is no exception - because it's Turing I made exception to my usual personal hard-ban on reading Wolfram. It's no exception to the above. It is, however, interesting despite being arrogant and self-promotional.
If you asked Stephen Wolfram what time it was, he would be arrogant and self-promotional, and mention Mathematica at least as much as the time.
It’s definitely self-promotion, but I don’t see why this is a bad thing. He’s clearly spent a large portion of his life developing a programming and computing environment to handle mathematics (and other things). What is he supposed to do? Write a blog post about something he's interested in, without using the programming language he has intentionally developed to deal with the things he’s interested in?
> So, OK, if I mounted a project to try to find the fundamental theory of physics, what would I actually do? It’s a complex project, that’ll need not just me, but a diverse team of talented other people too.
It's illuminating that, in order to explore the nature of space and time, he mentions Euclid, Einstein, but most of all himself and his work. The self-absorption encompasses all of existence.
That said, dismissing all of his writing as "arrogant content marketing blogspam" feels uncharitable and too reductive - I don't disagree, but still consider it arrogant self-promotion of the highest order, by one of the most productive and insightful thinkers of our time.
You manage to neatly encapsulate why I find him so frustrating.
"feels uncharitable and too reductive"
I'm old enough to remember when the law suits, a flagged throwaway comment briefly mentions, were going - my recollection is of a lengthy effort to deprive the other developers of the fruits of Mathematica labours. That colours later impressions. Charitable isn't necessarily always the right take...
Still, that's an aside here, and perhaps I was too sweeping. It's difficult as there are rare times, like this one, where the topic is fascinating and well explored, and the self-promotion is, for Stephen, light touch. It's well known he was a child prodigy, so I'm sure many people and events had part in boosting his ego and innate sense of exceptionalism, resulting in the personality we know. So I don't entirely blame him for it...
"arrogant self-promotion of the highest order, by one of the most productive and insightful thinkers of our time."
You're not wrong. He'd probably be well served employing someone to bring a lighter touch, via an editing pass to all output. I end up not finishing articles he writes on topics I might otherwise find hugely interesting. Solely because too much prose is spent telling me he's brilliant, rather than simply showing it. For me at least, the style of delivery has cost the message - as I stopped regularly reading him as far too frustrating, ages ago. :)
Ehhh, you know, he's not a journalist. He's the founder and CEO of a company that he is very hands on at. What you view as arrogance and self-promotion is really just a man who is obsessed with the technology he builds and works on every single day. No one is forcing you to read his stuff or pay attention to him.
I found his relentless self-promotion really distracting and annoying. And presenting lambda calculus in terms of his own language only makes it more confusing.
However, I am impressed with the tenacity it took to trace the paper to its origin and there's a lot of interesting story in the process.
This seems unsurprising to me. Presumably the language he designed fits his way of thinking, and he uses it to express his thoughts.
As long as you still understand it he succeeded in using it to communicate, and with some people that's a lot better than them not communicating at all because they have to use someone else's language.
If someone comes up with an amazing construct in an invented language and gets any outside eyeballs on it that can understand it, someone will transcribe it into a more common notation anyways.
“Made-up language” is a bit harsh. The Mathematica company has hundreds of millions of dollars of revenue, right? It makes sense for his public communications to use it, just like you’d expect to see the guy who wrote Haskell to give examples in Haskell.
Have a look at this page [1]. Mathematica is exceptionally powerful and has a very rich vocabulary. In so far as expressing ideas across the computational paradigms - you will struggle to find a match.
It's just a pity that its grammar/syntax is unintuitive to people who come from conventional programming languages.
My unpopular opinion is that Stephen Wolfram doesn't get enough credit. Yes, he has a large ego, but he remains one of the most remarkable people in science today.
Can you state in a few lines what you think he should get more credit for?
He's an interesting guy, a good businessman, and I enjoy reading his anecdotes, but I kinda figure he gets about the right amount of credit for his achievements.
If you mean "new kind of science" for example -I think he got about what he deserved on that.
You shouldn't judge the value of conjectures until you know whether they're true or not. Right now, we have no computable model for physics. NKS conjectures that some particular types of CA could compute our universe. If this turns out to be true, it'll be huge.
I dunno, I think it's pretty easy to judge the value of not easily testable wacky conjectures. I don't think much of Penrose's idea that brains are quantum gravitic computers either, and that is vastly more close to being testable, and Penrose's achievements and track record in actual science are also vastly more impressive.
Putting that aside; computer guys seem to think "computability" is important in physics. I don't. The strong Church Turing thesis is an ideological idea, not a physical one. In fact, it is an ideological idea with very little evidence in its favor either in computer science or in the world of matter.
The conjecture that our universe is isomorphic to a CA is absolutely testable. When we find a CA that behaves just like the universe, we'll know it's true. If we find a completely different way of computing it that doesn't map to a CA, we'll know it's false.
Computable physics would be extremely useful. Even with coarse approximations you can only integrate the Schrödinger equation among hundreds of particles. So you can't do accurate computational biochemistry except maybe one small molecule at a time.
>"If we find a completely different way of computing [the universe]"
We can only compute models of the universe. If a model apparently never contradicts our observations of the universe, then we lazily identify the universe with the model within casual contexts, but we don't actually take that as Absolute Truth. Thus, within appropriate contexts, we might speak as if the "forces" of Newton are actual platonic things, as if the arrows in a freshman physics textbook actually exist and could poke you in the eye. But they don't, they are merely a model.
So, suppose we discover tomorrow a new equation which seems to match all observations, and which we can formally prove transcends CAs. Well, we'll never know whether or not tomorrow we'll find an instance where that new equation breaks down, and has to be replaced by an updated equation which IS computable by CAs. Thus, your supposed "test" is not a test at all.
>Computable physics would be extremely useful. Even with coarse approximations you can only integrate the Schrödinger equation among hundreds of particles
You seem to be confusing "computable" with "efficiently computable" or something. A function can be computable but still be prohibitively expensive to compute.
OK, I agree that finding a non-CA way of computing physics doesn't necessarily rule out a future CA model being better.
Current physics models (integrating the Schrödinger equation) aren't computable even in principle, because they involve infinite continuous vector spaces. So a CA model is a theoretical breakthrough because it's computable, even if it's not efficient.
Numerically integrating the Schrödinger equation scales exponentially in the number of quantum states, while the CAs proposed in NKS only scale with the volume of space, so there is some size of system where it'll beat numerical integration.
> ... Computable physics would be extremely useful.
Yeah, undoubtedly, but that has nothing to do with it being true.
Wolfram doesn't make the case, at all, that it might be true, nor does he suggest any reason a CA might be a better model than the Schroedinger equation, or a way of searching for CA oriented models. The fact that modeling physical equations is difficult on a Turing machine is probably telling you something interesting about nature, rather than telling you to dispose of equations as models of reality.
The whole thing is about as useful as Tipler's idea that God is a supercomputer at the end of the universe. Maybe thought provoking for certain kinds of people, but not helpful at all in the business of figuring out how the universe works, or useful things to do on a computer. It's basically an exotic form of science fiction with a higher than average cognitive load.
> If we find a completely different way of computing it that doesn't map to a CA, we'll know it's false.
This is wrong. You would have to additionally prove that the other thing is the only alternative.
Also, CA is not testable in the sense that the theory of relativity is testable. The latter makes measurable predictions that can be satisfied, the former does not. I can imagine any model - unicorns and fairies included - and say that is behaves like the universe. The only way to falsify my claim is to empirically contradict one of my claims. NKS does not put forth such claims. Not the kind you would build a new CERN for.
A CA model of physics would certainly make measurable predictions, probably including some surprising ones that would suggest experiments to confirm them.
Where do you take your certainess from? If even Stephen Wolfram could not produce such predictions, then I doubt anyone else could. In all likelyhood, it is just not a good physical model.
> This is wrong. You would have to additionally prove that the other thing is the only alternative.
A CA theory of physics would just be math, right? Wouldn't it end up being isomorphic with some mathematical representation, albeit perhaps easier to understand or evaluate in its CA form?
What if it's discrete but effectively matches what we know in that current mathematical methods correctly approximate it in their respective contexts and resolutions? I mean in the same sense that Newtonian physics approximates Einsteinian physics at low speeds and distances.
Wouldn't a truly non-quantized field or dimension falsify this idea? AFAIK there are none known yet, though there are some (like time) where we don't know.
> I dunno, I think it's pretty easy to judge the value of not easily testable wacky conjectures.
Can you describe the process you use to easily judge the value of such conjectures? I'm at a loss of how that would be done since, even though a conjecture might not be testable easily, it might still end up being true.
Even if not completely true, it might in some sense be close enough to inspire new ways of thinking that ultimately lead to the correct solution. For this reason, I'm wary of premature dismissal of "wacky" ideas.
> Putting that aside; computer guys seem to think "computability" is important in physics. I don't.
Taking a step back, the very ability to realize computational systems in physical systems seems very peculiar and interesting in itself, in the same way that noticing how peculiar it is that mathematics is able to describe such a large portion (all?) of physics. It then seems natural to ask oneself whether any physical system could then be considered to model some computation, which would make the connection bidirectional. I do not consider this observation to be that ludicrous nor exclusive to the computer guys.
I agree. It's a tough one because his ego is so huge he's often accused of taking credit for other peoples' work. My impression from reading through A New Kind of Science is that it wasn't some plot by him to take credit for the whole of CA research but that his ego just kind of caused him to write in such a way as to give that impression.
All personalities aside, I feel like the core thesis of this and other books on CAs, fractals, computational physics, etc., are sort of like the edges of some higher scientific theory that we don't yet understand. The entire universe looks like a big fractal with structures repeating with some variation at different scales, and we don't "get" this beyond hand-wavey pure speculation that starts sounding like New Age babble. I wonder if we're just at the edge of being smart enough to grasp this higher order of understanding and if we did we'd have among other things a unified theory of physics. It makes me think of what chimpanzees might feel when we try to teach them language and basic mathematics. They can almost get it.
Maybe there are beings out there that "get it" and they're out there doing things that to us would be indistinguishable from magic.
Some folks here enjoy reading it but Wolfman is often out of line when putting his comments and twists in. It also displays a creepy nature of wolfman to want to know very personal things.
Example, recording private phone calls and releasing them to the public or releasing those to lawyers when he feels they might serve his purpose.
Creepy and borderline dangerous. But for the average Joe all this seems to be enjoyable.
I am far enough away from that part of my life, I apologize for not being able to give a more detailed and convincing testimonial for this book.