Althouse: "The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought."

२५ जुलै, २०१९

"The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought."

"The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be ‘voluntarily’ reproduced and combined."

Said Albert Einstein, quoted in "The Weil Conjectures: On Math and the Pursuit of the Unknown" by Karen Olsson.

Einstein — participating in a study of the working methods of mathemeticians — was responding to the prompt: "It would be very helpful for the purpose of psychological investigation to know what internal or mental images, what kind of 'internal world' mathematicians make use of..."

Olsson writes more generally, not just of mathematicians: "If only we had more access to the untranslated thoughts, to the mystery of how the mind churns."

५६ टिप्पण्या:

MikeR म्हणाले...: When I was young someone did a study of chess grandmasters. They asked them and also other lesser players to describe their thought processes as they examined a position. They found out that grandmaasters weren't especially better than everyone else in the description phase. But there were a few seconds at the beginning of a new position where the grandmasters could not describe what they were doing at all. When those seconds were over, they already had a good idea of what was happening, way better than the other players.; २५/७/१९, ८:३३ AM
tim maguire म्हणाले...: I don't think you can learn much about how people think by asking them.; २५/७/१९, ८:३५ AM
traditionalguy म्हणाले...: Psychical entities are what we call spirits. Duh. The Mind of God gets shared that way.; २५/७/१९, ८:३८ AM
The Cracker Emcee Refulgent म्हणाले...: Genius is enhanced perception, not necessarily the cogitation that follows. Thought that begins on third base.

Ask me how I know.; २५/७/१९, ८:३९ AM
Fernandinande म्हणाले...: Einstein's full(er?) answer is here.; २५/७/१९, ८:४३ AM
Fernandinande म्हणाले...: Duh. The Mind of God gets shared that way.

That explains why most people are stupid.; २५/७/१९, ८:४६ AM
Owen म्हणाले...: Words are way downstream of what happens. Music is maybe closest? For me drawing summons an entirely different mental process. So might rowing when one is truly “in the zone.” But here we are, stuck using words to describe all that; these little hardened clinkers from the fire.; २५/७/१९, ८:४७ AM
Wince म्हणाले...: In other words, they're just totally intuit?; २५/७/१९, ८:४७ AM
Lucid-Ideas म्हणाले...: Einstein and another polymath - John Von Neumann - would often describe their interpretations to laymen as 'imagine that...' or 'imagine this...'.

Einstein and those that taught special relativity early on used to use precisely those terms in trying to translate the mathematical concepts to colleagues or pupils.

John Von Neumann used to translate mathematical computations on the explosive 'lenses' and wave shaping of the atomic bomb to others at Los Alamos in exactly the same way, almost like they had a complex visual computer model already formed and they were trying to 'get it out' at a time when the technology to express it didn't exist yet.

Fascinating.; २५/७/१९, ८:४९ AM
Lucid-Ideas म्हणाले...: I imagine hyper-genius polymaths often have these concepts show up unannounced, as if by magic and that very often they're simply using math and computation as a way to express a concept already present in the mind.

Very much like a lucid idea (lucid = bright) or similar to the Buddhist concept of revealed enlightenment. It just happens and you spend many years and hours trying to explain 'why' afterwards, especially to lesser mortals.

I also think that's why so many other aspects of their lives appear disheveled. From Turing to Sagan, their day-to-day/hour-to-hour lives really are a ramble, as if life itself doesn't measure up to anything substantial worth a minutes thought.; २५/७/१९, ८:५४ AM
Ken B म्हणाले...: Nonsense. Thought consists of chunks of 280 characters or less. It used to be 144 or less, which explains why our society is so much better at thinking than it used to be.; २५/७/१९, ८:५७ AM
Crimso म्हणाले...: Edward Teller on von Neumann:

"[He] would carry on a conversation with my 3-year-old son, and the two of them would talk as equals, and I sometimes wondered if he used the same principle when he talked to the rest of us.”; २५/७/१९, ९:०० AM
Maillard Reactionary म्हणाले...: C.E. Refulgent's comment coincides with my personal experience. When I was doing circuits and systems engineering we would sometimes have very puzzling, intermittent problems that were very hard to diagnose and resolve. I could often get an insight into where to look by visualizing the whole system and its interacting parts and how they behaved in time. Note that I use "visualize" for lack of a better term. Generally, there was no visual imagery per se involved.

So many times the cause of a problem would suddenly occur to me at home, hours later, not prompted by thinking about it at all. Some part of my mind was working on it below my awareness. These insights were nearly always correct.

I do a similar thing these days when I am photographing. I never look for specific subjects or try to arrange images according to any "rules of composition". I just move the camera around (sometimes changing the lens I'm using) until the image "clicks in". There is no explicit thought process involved at all.

Recent experiments where subjects have to react with some action to stimuli seem to show that part of the brain decides what to do and begins to get the motor processes working a quarter-second or so before the conscious mind becomes aware of having chosen a course of action. (We have all experienced this when we touch something hot!)

There's a lot going on under the hood in the brain, and we're very early in figuring it out. I suspect that what we usually think of as consciousness is only a small part of it.; २५/७/१९, ९:०० AM
narayanan म्हणाले...: In Introduction to Objectivist Epistemology,

Rand introduces her theory of knowledge by means of its central feature,

a new theory of the nature and formation of concepts.

Along the way, she provides her fundamental

answer to the Kantian turn in epistemology,

offering a non-skeptical, non-mystical approach to knowledge.

__________________

if you have read it - whatchall think?; २५/७/१९, ९:०२ AM
daskol म्हणाले...: Images, dreams, symbols and patterns. Linking Damasio's brain model to MBTI/Jungian type theory, intuitive types (particularly Ni) are often "picture thinkers" and Damasio might say such people have a more direct brain link to the internal components of the somatic markers that guide decision making. The images and patterns and symbol fragments are accessible, leading to a "Eureka!" feeling making it difficult to understand how one has come to know something, let alone explain it to others or describe the process by which knowledge came to be. God only knows what goes on in a brain like Einstein's, which was not only incredibly "creative" but also super-charged.

One thing I've noticed consistently about my own more pedestrian thought process is that when I'm communicating, I often confuse people because I begin with the end and get to the beginning only at the end of my discursion. When it comes to written communication, that's easy enough to fix: write the content out and then simply reverse the order, so that the last sentences and paragraph go first and the first thing written usually serves as the conclusion.; २५/७/१९, ९:०३ AM
Francisco D म्हणाले...: There is some evidence that knowledge is stored in our synapses. Synaptic connections come from the experience of reading, doing, listening, thinking, etc. "Smart" people have better synaptic connections than not-so-smart people. However, that does not mean that they have strong conscious awareness of these connections.

It is not unlike "muscle memory" for athletes. The more we exercise the brain in a somewhat disciplined manner, the more we have effective learned cognitive routines. IMHO, there are better and worse routines, but there is no best one. That is why the brains of scientists, lawyers, artists and others have different routines and different knowledge.

I am sure the there are neuroscientists out there who have a much different view. Right now, we are all just theorizing based on extremest incomplete data.; २५/७/१९, ९:०६ AM
traditionalguy म्हणाले...: Seriously,this is how "progress" happens. I loved the two James Bourke series "Connections'and "The day the Universe Changed." They are worth watching. And they are how God blesses men.; २५/७/१९, ९:०८ AM
Amexpat म्हणाले...: Two thoughts:

I'm bilingual and I often get asked by monolinguals which language I think in. My response is that I don't normally think in any language. The only time I think with a language is when I'm working out how to say something. But that often has to do with how to present a conclusion that I reached with deeper, non-lingual thinking.

I read that Einstein was very late to start talking as a child. Could be that he was more interesting in pursuing pure thought rather than communicating his thoughts to others.; २५/७/१९, ९:०९ AM
Jaq म्हणाले...: If you read Zen and the Art of Motorcycle Maintenance there are some interesting ideas. Of course the book is mostly crackpot, which carries the idea much further than can be supported by logic, which, not surprisingly, the author rejects.

But it’s true that if you immerse yourself in a problem space for many years, answers to queries will come to you almost unbidden. I used to work with a database tech which at the time we called “cubes” which basically calculated answers to all possible questions, within certain parameters, of course, and stored them so that when you queried it, the answer would be there almost instantly, since it didn’t have to be calculated real time, it already had been by background processes.

I always thought that this was the reason that Gov Rick Perry froze on stage on that question, he was used to thinking about the issue, but had never put his thinking into words.; २५/७/१९, ९:१० AM
traditionalguy म्हणाले...: NB:These blessings from God always come through chosen men. They don't rain down from outer space.; २५/७/१९, ९:१० AM
joshbraid म्हणाले...: I had the privilege of attending seminars by and working (briefly) with Edsger W. Dykstra. He won the first Turing award for his introduction of the concept of semaphores into Operating Systems theory. He said he got the idea by study the methods that the Dutch railways used to keep their trains from crashing into each other when using single tracking along their routes. He used to teach sorting algorithms by using the visual image of strings of different length, hanging them together and "seeing" which one was longest. Amazingly brilliant in the same way. So many of his descriptions were visual--easy to comprehend, hard to duplicate.; २५/७/१९, ९:१२ AM
Jaq म्हणाले...: Sometimes I think that Einstein’s biggest breakthroughs came because he believed the result of his own math, when so many refused to believe it, and he was aware of his assumptions.; २५/७/१९, ९:१३ AM
buwaya म्हणाले...: I sympathize.
I cannot think at an Einsteinian level, but my poor brain also runs into these rocks.
I find language an obstruction.
Thats why I am addicted to my crutch, the whiteboard.
It is much better at describing systems and processes.; २५/७/१९, ९:१५ AM
Jaq म्हणाले...: “He used to teach sorting algorithms by using the visual image of strings of different length, hanging them together and "seeing" which one was longest.”

So how does that get applied in practice using a computer?

"He said he got the idea by study the methods that the Dutch railways used to keep their trains from crashing into each other when using single tracking along their routes.”

Phone systems used this metaphor a long time ago, a long long time ago.; २५/७/१९, ९:१८ AM
Big Mike म्हणाले...: When I proved theorems I would “see” a key step that I somehow knew was going to come in the middle of the proof. I still had to deduce the steps leading from the initial conditions to the key step, then from the key step to the conclusion. I always figured this was just a trick I had learned for blasting through math homework — if the latest chapter in the textbook covered l’Hospital’s Rule, then the key step probably used l’Hospital’s Rule. That sort of thing. It was a real delight when I discovered I could still do that when working on proofs where I did not have a textbook to provide hints to me.

But the best mathematicians don’t seem to see “the” key step; they seem to see multiple keys without knowing what they see or how they tie together.; २५/७/१९, ९:१९ AM
n.n म्हणाले...: "Duh. The Mind of God gets shared that way."

That explains why most people are stupid.

Conflation of logical domains or an alternative faith (e.g. atheism, agnosticism). There are few people who will limit their speculation to the near-domain or the so-called "scientific domain", where everything is observable, reproducible, without liberal assumptions/assertions. As for the mind, science cannot discern between origin and expression, but relies on correlations to realize a measure of consistency.; २५/७/१९, ९:२२ AM
Jaq म्हणाले...: I am pretty sure that there is a huge disparity in male and female thinking along these lines. “Where are those blueberries going to be this year?” is a far different question than “Where are those bison going to be tomorrow.”

Oh, I forgot, evolution never happened.; २५/७/१९, ९:२२ AM
Mike (MJB Wolf) म्हणाले...: For some reason this brings to mind the Nachman Stories by Leonard Michaels.; २५/७/१९, ९:२५ AM
n.n म्हणाले...: the whiteboard. It is much better at describing systems and processes.

You can model it with numeric or linguistic speech, or visualize it in your mind, but it becomes unwieldy directly proportional to complexity.; २५/७/१९, ९:२५ AM
Jaq म्हणाले...: Evolution involves the “invisible hand” of natural selection, just like the so called science of economics, and we all know that that is make believe rationalization. Obviously somebody is in charge of the whole thing!; २५/७/१९, ९:२६ AM
Char Char Binks, Esq. म्हणाले...: Math is simply a higher level of thinking than most people are accustomed to, or capable of. Higher math simply can't be expressed in ordinary language -- that's why it exists, and why it has its own symbols and grammar that are mostly beyond the ken of the average person, including me.; २५/७/१९, ९:२७ AM
Nonapod म्हणाले...: I remember a while back watching some documentary about child prodigies, savants, and geniuses where they were comparing the brain scans of normal people and savants as they were working through different problems. For example, I think there was this person who could almost instantly tell you what day of the week it was or would be if you gave them some date at random.

Basically what they noticed was that different areas of the brain would "light up" (more blood flow or whatever) in savants that wouldn't in a "normal" people when they were thinking about certain problems. I think it was presumed that the activity in the areas in question were most likely happening at a subconscious level. In short, it was just happening without specific concious direction. If this is indeed what's going on, it may explain why so many gifted people are often unable to clearly describe their internal processes... they literally don't know what's going on since it's happening beyond their awareness.

As an analogy, it's like if you had a calculator built in to you brain that you could feed inputs and it would return outputs. You might not have any idea what the calculators doing.; २५/७/१९, ९:३२ AM
iowan2 म्हणाले...: Sherlock Holmes said sluething is easy. "Eliminate the impossible, everything else is open to examination."
It is surpising how many people waste time examining the impossible.

I find my self limiting my conclusions, statments, opinions, first run through a simple test of my ability to defend myself. If I cant defend my actions, I only take them if I accept the blow back. Which sometimes I am willing.; २५/७/१९, ९:३३ AM
sinz52 म्हणाले...: AAT: "I am pretty sure that there is a huge disparity in male and female thinking along these lines."

No way to prove or disprove that. As this article shows, we don't really know just what any creative person is thinking (and even the person may not understand it).

What we do know is that there is a disparity in male and female *writing* -- even on highly technical subjects like mathematics. Analysis of many technical papers has shown that male authors don't write like female authors.

http://www.cs.biu.ac.il/~koppel/papers/male-female-text-final.pdf; २५/७/१९, ९:४५ AM
Mr. Forward म्हणाले...: “The Index of Untranslated Thoughts”; २५/७/१९, ९:५६ AM
rhhardin म्हणाले...: That was before Wittgenstein; and even today Wittgenstein isn't understood.

You could have said to Einstein that language reasoning has both a covariant and a contravariant part. You don't notice the one you see with, in favor of what you see with it.; २५/७/१९, १०:११ AM
Jaq म्हणाले...: “It is surpising how many people waste time examining the impossible. “

A lot of people accused Einstein of that.; २५/७/१९, १०:१४ AM
rhhardin म्हणाले...: French is the most natural language, because the words occur in the same order as the thoughts. Some Frenchman observed that.; २५/७/१९, १०:२४ AM
joshbraid म्हणाले...: "Phone systems used this metaphor a long time ago, a long long time ago."

The Dutch railway system is much likely older than a "phone system". And, yes, your point is true, that such solutions are found over and over historically. The real genius is imagining something new using images and patterns from something old. For example, one way I was taught relativity using the image of a bus traveling at the speed of light while looking back at a clock at the point of origin. Such a simple model yet I would never have thought of that, even after running through the differential equations in physics for relativity.; २५/७/१९, १०:२८ AM
Jaq म्हणाले...: "French is the most natural language, because the words occur in the same order as the thoughts. Some Frenchman observed that.”

OK, that’s my laugh out loud for the day.; २५/७/१९, १०:३१ AM
rcocean म्हणाले...: Wiel, what of it?; २५/७/१९, १०:३९ AM
daskol म्हणाले...: Hey, this thread is about thought apart from language, not the way in which a language like French may influence thought, or the way in which expression in a particular language gives tendencies to thought.; २५/७/१९, १०:५१ AM
Sebastian म्हणाले...: Question for Olsson readers: does she actually know any math, like, real math?; २५/७/१९, १०:५४ AM
Mike (MJB Wolf) म्हणाले...: I guess it’s the title of Wiel’s article that conjure up allusions to Michael’s The Penultimate Conjecture”, which is about a mathematician who thinks differently.; २५/७/१९, १०:५५ AM
Narr म्हणाले...: There's a thing inside my brain.
There is a thing inside my brain.
Inside the brain, of the thing, inside my brain,
There is a thing.

Inside the brain, of the thing, inside my brain,
There is a thing.

Inside the brain, of the thing, inside the brain,
of the thing, inside my brain,
There is a thing.

Inside the brain, of the thing, inside the brain,
of the thing, inside the brain, of the thing, inside my brain,
There is a thing.

[etc]

Narr
Recursion, take me away!; २५/७/१९, ११:२८ AM
Roy Lofquist म्हणाले...: “Sir Isaac Newton, renowned inventor of the milled-edge coin and the catflap!"

"The what?" said Richard.

"The catflap! A device of the utmost cunning, perspicuity and invention. It is a door within a door, you see, a ..."

"Yes," said Richard, "there was also the small matter of gravity."

"Gravity," said Dirk with a slightly dismissed shrug, "yes, there was that as well, I suppose. Though that, of course, was merely a discovery. It was there to be discovered." ... "You see?" he said dropping his cigarette butt, "They even keep it on at weekends. Someone was bound to notice sooner or later. But the catflap ... ah, there is a very different matter. Invention, pure creative invention. It is a door within a door, you see.”
― Douglas Adams, Dirk Gently's Holistic Detective Agency; २५/७/१९, ११:३८ AM
Howard म्हणाले...: Blogger Lucid-Ideas said......almost like they had a complex visual computer model already formed and they were trying to 'get it out' at a time when the technology to express it didn't exist yet.

Visualization is a common and powerful problem solving technique. I think this is an evolutionary advantage men have in most STEM subjects.; २५/७/१९, ११:३८ AM
Howard म्हणाले...: Maybe I've turned into a Russian bot since I am agreeing with everything AAT says.; २५/७/१९, ११:४२ AM
Owen म्हणाले...: The visual cortex is a very big piece of real estate. Suggesting that it has high survival value. But is the cortex activated only by optical inputs? When we acquire “insights” or “imagine” some problem, do we not activate the visual cortex or some other ancillary/analogous structure and process? We live in a 4-D world of space and time and MUCH of our cortical effort aligns with mapping ourselves (and whatever we are hunting or protecting) in space and across time. And when we are trying to think abstractly, about the hands of a clock in a train station exactly as something occurs elsewhere, we are using those preexisting cerebral circuits and patterns. Only now for a “pretend” run-through of how it would evolve.

It is said that Richard Feynman used to get stopped by cops late at night when he was walking around Cambridge talking to himself and moving his hands to depict (for himself, working out some idea) how a particle might move in a field. That ability to “just suppose” is IMHO critical to this kind of intelligence.; २५/७/१९, ११:५० AM
Big Mike म्हणाले...: The more I read about Simone Weil the sadder I feel. I am not that far into the book, but it seems clear to me that she could have been a great scientist or, more likely, a great mathematician except that her parents prevented her, apparently on the grounds that mathematics was not an appropriate field of study for a girl the way it was for her brother Andre. This despite the prior existence of female French mathematicians such as Émilie du Châtelet and female physical chemist Marie Curie. Infuriating to me, because the world is not blessed with enough real mathematicians as it is. Ignoring her brain, wired for mathematics (so we suppose), because of her ovaries is simply insane

Sebastian asks whether Olsson is herself a mathematician. My take (and I am not very far into the book) is that Olsson realizes early on that her brain is not quite wired the same way as true mathematicians’ brains are. Nor is it wired for engineering.; २५/७/१९, ११:५१ AM
Yancey Ward म्हणाले...: I am an avid puzzle solver- crossword puzzles, math problems, riddles, chess problems etc. I can't easily tell you how I arrive at a solution for any of them. In the case of crossword puzzles, if I get stuck, it is always better for me to put the puzzle down and not think about it and do something else. Almost always, I will just suddenly realize what the solution is without having consciously thought about it at the time.

When I was a chemist, I usually solved tough problems the exact same way- I would study the problem until I was sure I understood exactly what the issues were, and then not think about it for a while, then remind myself of the problem and then do something else- I often would wake up in the middle of the night with a good idea for solving them, or I would be reading a book on something completely different and all of a sudden get an inspiration. Again, I don't know where they came from.; २५/७/१९, १२:०७ PM
Marc in Eugene म्हणाले...: H.R. Hamilton explained to Einstein how this works, but Einstein couldn't quite grasp it all.; २५/७/१९, १२:३१ PM
daskol म्हणाले...: I once had the disconcerting though pleasant experience of somebody not just reading my mind, but actually seeing the picture I was imagining in my head as I explained something.; २५/७/१९, १:३७ PM
Maillard Reactionary म्हणाले...: joshbraid @9:12 AM: Very cool that you knew Dykstra a bit. It is interesting that the problem of implementing provably reliable concurrent software systems was solved so relatively recently.

I learned about implementing concurrency by studying Per Brich Hansen's Operating System Principles, which owed a lot to Dysktra's pioneering work. Once it clicked it was like a light went on in my head. Designs that would otherwise have been intractably complex and error-prone could instead be done in a way that was orderly, lucid, reliable, and sometimes even elegant.

Nowadays with basically unlimited memory, gigahertz multiprocessor cores, and layer upon layer of runtime code, language interpreters, and the rest of it, it seems that many software engineers have no idea of what's going on below the source code level, and seem to think that's fine. I'm not sure what to make of all that but their work product certainly isn't more reliable than the best of what was done in the '80s and '90s. (A software engineering euphemism these days is "technical debt" == "problems we'll let the customers find for us and fix later, maybe".); २५/७/१९, ४:४४ PM
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Narr म्हणाले...: I fell for that JAMES ANDERSON pitch once! Don't do it, friends.

Narr
I'll never see that $499 again, I'm pretty sure.; २५/७/१९, १०:०६ PM