An Educational Singularity
post by lsusr
score: 3 (5 votes) ·
The educational phase transition
An alternative model
Knowledge compounds. Painting is good practice for architecture. Stand-up comedy is good training for stage magic.
The knowledge transference between math and physics might be as high as 75%. Unfortunately, the knowledge transference between two random fields tends to be small. Between math and drawing it might be as low as 1%. In my personal experience it's hard to find any pair of broadly applicable subjects that don't have at least 1% overlap. Usually the number will be between 1% and 75%.
Let's suppose mastering a new field of knowledge gives you a 5% discount on average on every subsequent field. Suppose it takes time for someone who knows nothing to master a new field. Then the amount of time it takes to master a new field is a function of how many fields you have already mastered .
How much time does it take to learn fields instead of just the field ?
This is a geometric series.
appears to converge.
converges for every positive transference rate. If we use 1% instead of 5% we just get .
What does this mean?
The educational phase transition
Obviously, someone who has hit is not going to possess all of human knowledge. No matter how much you know it's still going to take you some minimum time to learn the dialectical quirks of, say, Hejazi Arabic.
What really means is you've hit a certain endgame. The process of learning has undergone a phase transition. All the broad conceptual machinery and widely-applicable facts are there. Picking up anything new is just a matter of plugging new data into preexisting sockets.
More interesting than "what happens at this phase transition" is the idea that "there is a phase transition" and we can reach it in finite time. Perhaps even within a human lifetime.
Much like stream entry, I suspect anyone who achieves this phase transition is better off keeping his/her mouth shut about it in polite society.
An alternative model
The concept of a singularity in the above model relies on a double-positive feedback loop. It assumes "Each subject you know conveys a compounding 5% discount on learning each subsequent subject." If we tweak this assumption into "Each of study time conveys a compounding 5% discount on learning each subsequent subject" then never converges as .
However, this alternative model still breaks down at high . It just breaks down gradually. For example, at the exponential model predicts an absurd learning rate times that of a beginner. In the human world such a high rate of learning is indistinguishable from infinity. The model has broken down.
Comments sorted by top scores.
comment by Viliam
· score: 9 (3 votes) · LW
Is "knowledge transference" a real thing, or one of those thousand things that didn't replicate? There are many myths in education, I wonder if this is one of them.
(I tried Wikipedia, but it only has an article on "knowledge transfer", which is about sharing information between people within an organization, i.e. something completely different.)
Bryan Caplan in The Case Against Education writes:
[Teachers say:] A history class can teach critical thinking; a science class can teach logic. Thinking—all thinking—builds mental muscles. The bigger students’ mental muscles, the better they’ll be at whatever job they eventually land.
[Is it true?] For the most part, no. Educational psychologists who specialize in “transfer of learning” have measured the hidden intellectual benefits of education for over a century. Their chief discovery: education is narrow. As a rule, students learn only the material you specifically teach them . . . if you’re lucky. In the words of educational psychologists Perkins and Salomon, “Besides just plain forgetting, people commonly fail to marshal what they know effectively in situations outside the classroom or in other classes in different disciplines. The bridge from school to beyond or from this subject to that other is a bridge too far.”
Many experiments study transfer of learning under seemingly ideal conditions. Researchers teach subjects how to answer Question A. Then they immediately ask their subjects Question B, which can be handily solved using the same approach as Question A. Unless A and B look alike on the surface, or subjects get a heavy-handed hint to apply the same approach, learning how to solve Question A rarely helps subjects answer Question B.
[In an experiment when subjects are told a military puzzle and its solution, and then a medical puzzle which can be solved analogically,] A typical success rate is 30%. Since about 10% of subjects who don’t hear the military problem offer the convergence solution, only one in five subjects transferred what they learned. To reach a high (roughly 75%) success rate, you need to teach subjects the first story, then bluntly tell them to use the first story to solve the second.
To repeat, such experiments measure how humans “learn how to think” under ideal conditions: teach A, immediately ask B, then see if subjects use A to solve B. Researchers are leading the witness. As psychologist Douglas Detterman remarks: "Teaching the principle in close association with testing transfer is not very different from telling subjects that they should use the principle just taught. Telling subjects to use a principle is not transfer. It is following instructions."
Under less promising conditions, transfer is predictably even worse. Making the surface features of A and B less similar impedes transfer. Adding a time delay between teaching A and testing B impedes transfer. Teaching A, then teaching an irrelevant distracter problem, then testing B, impedes transfer. Teaching A in a classroom, then testing B in the real world impedes transfer. Having one person teach A and another person test B impedes transfer.
[...] No wonder even transfer optimists like Robert Haskell lament: "Despite the importance of transfer of learning, research findings over the past nine decades clearly show that as individuals, and as educational institutions, we have failed to achieve transfer of learning on any significant level."
[...] Counterexamples do exist, but compared to teachers’ high hopes, effects are modest, narrow, and often only in one direction. One experiment randomly taught one of two structurally equivalent topics: (a) the algebra of arithmetic progression, or (b) the physics of constant acceleration. Researchers then asked algebra students to solve the physics problems, and physics students to solve the algebra problems. Only 10% of the physics students used what they learned to solve the algebra problems. But a remarkable 72% of the algebra students used what they learned to solve the physics problems. Applying abstract math to concrete physics comes much more naturally than generalizing from concrete physics to abstract math.
[...] Each major sharply improved on precisely one subtest. Social science and psychology majors became much better at statistical reasoning—the ability to apply “the law of large numbers and the regression or base rate principles” to both “scientific and everyday-life contexts.” Natural science and humanities majors became much better at conditional reasoning—the ability to correctly analyze “if . . . then” and “if and only if” problems. On remaining subtests, however, gains after three and half years of college were modest or nonexistent.
[...] Transfer researchers usually begin their careers as idealists. Before studying educational psychology, they take their power to “teach students how to think” for granted. When they discover the professional consensus against transfer, they think they can overturn it. Eventually, though, young researchers grow sadder and wiser. The scientific evidence wears them down—and their firsthand experience as educators finishes the job
Intuitively, it seems to me that having a good model of world trained on some subjects should provide some advantage at other subjects. But either it is an obvious prerequisite (such as: understanding chemistry helps you understand biochemistry) or the benefits are likely to be small (e.g. from physics I could learn that the universe follows relatively simple impersonal laws; but that alone does not tell me which laws are followed in sociology or computer science). Having good general knowledge can inoculate one against some fake theories (e.g. physics and chemistry against homeopathy), but after removing the fake frameworks there is still much to learn. Also, the transferred knowledge (e.g. "there is no supernatural, the nature follow impersonal laws") is the same for all natural sciences, so the "X%" you get from physics is the same as the "X%" you get from chemistry; you do not get "2X%" after learning both of them.
comment by gwern
· score: 5 (2 votes) · LW
Caplan is correct here. There's no 'far transfer' of the sort which might even slightly resemble 'get a 5% discount on all future fields you study'. (Not that we see anyone who exhibits such an 'educational singularity' in practice, anyway.) At best there might be a sort of meta-study-skill which gives a one-off 'far transfer' effect, like learning how to use search engines or spaced repetition, but it's quickly exhausted and of course just one doesn't give any singularity-esque effect.
A more plausible model would be one with pure near-transfer: every field has a few adjacent fields which give a say 5% near-transfer. So one could learn physics/chemistry/biology, for example, in 2.9x the time of 3 individuals learning the 3 fields separately at 3x the time.
comment by Slider
· score: 5 (4 votes) · LW
The model is very simple and the conclusion pretty far-reaching althought interesting. Rather than assume that the conclusion is true I would hunt for what modelling details were glossed over.
Say both painting and stand-up comedy teach self-expression. If magic utilises that then it doesn't double benefit from that. That is learning a field lowers how much other fields support learning of new fields.
I could also see how learning a field sements a mindset that makes it harder than completely naive person to learn something. Say a lawer benefits from a a mechanistic blind interpretation of rules and painting supports a impulsive reinterpretion and forfeiting rule use. The two experts teachings would actively resist the other kind of adatation. Now it might be it's own skill to not make them conflict that much or find the context barriers were one approach is applicable over the other. But this is still work over someone to whom the area is the only truth. That is while there might be "synergistic" pairs the probablility that you have "antisynergistic" pairs increases as you pick up fields.
Even if the simple analysis isn't ironglad ti is likely that the value of being a polymath is undervalued and the exact circumstances where it makes sense to adopt a polymath strategy rather than an expert strategy is not that widely discussed. Further complication to that is that a group of experts that have different areas of expertise is somewhat comparable to a group of homogenous polymaths. So even if moving to a more polymath strategy would make a single person more competent it's likely that being more starkly expert would increase the groups effectiveness if others can employ enough trust to get dominated by the opinions of the experts. This might also have it's own singularity conditions. That is at some point there is enough trust that any area you can train a single person to be a expert on, the group can be made to effectively have by adding a person to it.