Any theory which predicts that math/physics/cs/EE has few women is inherently flawed if it doesn't also predict that medicine/law/advertising have plenty of women.
I am not sure where you're going with this, but you can't make such a comparison at a given moment in time. The reason is that struggles usually follow power, and so it is likely that at any point in time, a marginalized group would concentrate its efforts to penetrate positions that imbue power. As the power structure shifts, so does the struggle. You can't equate professions that hold different amounts of power at different times. Certainly up until some decades ago, law and medicine carried much more prestige and influence -- and hence, power -- than math and the physical sciences. In fact, software's gain of prestige correlates quite well with the drop in women participation. It is quite anomalous in that the existence of the field long predated its power. Law and medicine, OTOH, are professions that have been seats of power for almost a millennium.
A model that correlates low female participation with high power -- and later, increased participation after a struggle -- predicts both observations. It is not such a surprising or sophisticated theory; historians have seen this pattern so often that it is almost banal. This pattern is so regular, that it's relatively easy for us to predict the future: fifty years from now, assuming the power wielded by software remains high, women participation will equal men's, and it will be hard for people to believe that that hasn't always been the case. Unfortunately, even though the result of the fight is certain, we still need to fight it. That is the price history exacts from us.
(I.e., I have no idea why you consider academic physics to have more power than academic biology.)
I also have no idea what you mean by "a marginalized group would concentrate its efforts". Are you implying that women don't make individual career choices based on their interest and aptitude, but instead "concentrate [their] efforts" in some sort of collectivist power grab?
That's a bit scary. I always thought women were just people like me, making selfish individual decisions to maximize their money/lifestyle/career enjoyment.
Certainly. Non-hegemonic groups are marginalized from seats of power. After a long struggle, they may increase participation. Put another way: groups with more power tend to preserve and increase the power difference between them and less powerful groups, while the less-powerful groups may gain a share of the power after a struggle.
Sadly, it's not my theory, but one of the most elementary theories -- backed by countless evidence -- of the social sciences, supported by studies in anthropology, sociology and history (with some backup from social psychology, too).
Can you state your theory clearly, or, at the very least, state what evidence compels you to doubt the current scientific consensus?
> Make sure to include a clear definition of "power", and make sure this definition is clear enough that I can at the very least evaluate "more" and "less" power.
I have done so on numerous occasions in the past in our conversations. Please refer to them or look up "power" on Wikipedia. The short description is influence, and if you'd like a description with a more quantitative "feel", I'd say the power a person has is the number of people they can influence indirectly (i.e. graph reach) summed over the magnitude in the change of behavior they cause in each affected individual.
> I.e., I have no idea why you consider academic physics to have more power than academic biology
I don't. See my other response to you.
> Are you implying that women don't make individual career choices based on their interest and aptitude, but instead "concentrate [their] efforts" in some sort of collectivist power grab?
I'm stating the much-observed, well-known fact, that society pushes and directs us in various directions. What we see as "free choice" is, in fact, "free choice under societal pressures and restrictions". That behavior is not collective but individual, only biased. Just like any fair coin is free to make a choice how to land, yet we can make very accurate predictions on the result of a thousand coin tosses. Collective behavior is not always the result of collective decisions.
> I always thought women were just people like me, making selfish individual decisions to maximize their money/lifestyle/career enjoyment.
All of us make selfish individual decisions, but the (probabilistic) fitness function is largely determined by large-scale, emergent properties of the system. Think of individual particle movement and temperature or of Brownian motion. There are no collective decisions involved -- only individual "decisions" and local interaction -- yet the end result is that global factors heavily influence the distribution in behavior of the individuals. The effect of social influence on personal choice has been heavily studied in social psychology, and, in fact, in zoology too.
Or men figure out the "thankless" part equally quickly but aren't as bothered to receive encouragement from others as the women?
The definition you give here almost does that, but how do I assign a number to "magnitude in the change of behavior"? You've not defined a "hegemonic group" either.
Anyway, since I can't quite understand your theory, maybe you can clearly state a hypothetical observation which would prove your theory incorrect. That's usually a good way to illustrate what a theory does and does not predict.
For example, to disprove my "more math less women" theory, you should find a broad category of similar careers, run linear regression on math content vs % female, and find a flat or upward sloping line. I.e., the same analysis as was done on Scott Alexander's post (see my link), but with the opposite result.
You don't. Read what I wrote.
> You've not defined a "hegemonic group" either.
If you're interested, look it up. I feel a strong sense of deja-vu.
> maybe you can clearly state a hypothetical observation which would prove your theory incorrect
I think I've done it twice in the past when talking to you, so I'll only provide a short abstract here (and again, it's not my theory but the consensus theory): If groups with power were not to resist social mobility (i.e. for less powerful groups to obtain more power) we'd see a constant shift in power distribution, which would be very fluid, while what we observe is the complete opposite: a very stable power structure that then breaks and gets restructured relatively very rapidly during revolutions that are rare. So the pattern is long periods of stability and then quick changes brought about by some explosive event or a demonstrable pattern of slow power acquisition through many struggles. When it comes to women, the pattern is often the latter (there's a simple explanation for that), but you can see how women gain access to politics, law, medicine etc. only after very long fights against very strong opposition (that invariably cite innate ability as the barrier).
> For example, to disprove my "more math less women" theory, you should find a broad category of similar careers, run linear regression on math content vs % female, and find a flat or upward sloping line. I.e., the same analysis as was done on Scott Alexander's post (see my link), but with the opposite result.
Two problems with that. First, yours is not a theory but a description. Second, it is not a very relevant one because it doesn't explain the constant change in participation, nor the gender-gap in the software industry. Finally, while "more math less women" may have always held on average, the slope has changed. I don't think anybody minds if the gender distribution in physics is 60-40%, even if that difference is entirely due to innate ability. So your description does not even compete with mine because it doesn't even try to explain the same phenomenon, which is the one we care the most to explain.
That has little to do with the 4:1 or even 10:1 difference we see in the software industry.
Then we are back to power being a non-ordinal concept.
...more power...
If power is not an ordinal concept, this phrase is meaningless.
I'm also confused as to how you can even determine that such a "constant shift" isn't happening - in terms of edges in your influence graph, they shift regularly. Yesterday I met a new person at work and we now interact and influence each other. The power digraph has gained 2 edges. Could you explain how you quantify this?
You're reading things that I'm not saying. It is an ordinal concept, but we don't have the ability to measure it well, only notice large differences. You can think of it as a quantity for which we have very inaccurate measurement devices.
> I'm also confused as to how you can even determine that such a "constant shift" isn't happening - in terms of edges in your influence graph, they shift regularly. Yesterday I met a new person at work and we now interact and influence each other. The power digraph has gained 2 edges. Could you explain how you quantify this?
Because in this discussion we are talking about groups (social mobility in individuals is an interesting, yet somewhat different discussion), and when we look at a large number of people, it's easier to approximate power through proxies such as income, percentage of powerful roles such as CEOs, leading journalists etc. (it's harder to compare power in individuals, because it's hard to tell which is more influential, a media personality or the CEO of a large company, especially as the latter's influence might sometimes be hidden).
Shifts in power from nobility to the bourgeois class, or in the relative cultural and technological power of Europe, were sudden changes of relative homeostases. Similarly, you can track power distribution between men and women, or between whites and blacks in the US. They point at very stable states that are violently changed, or (usually in the case of women), a faster rate of smaller revolutions (or a more steady rate of change). The difference between male/female and race hegemonies is also well understood (and seen in many other cultures), because the classification of women as "strangers" is always very different from that of actual foreign ethnicities.
You now say this: "it's easier to approximate power through proxies such as income, percentage of powerful roles"
Lets work with this specific prediction. If a group has a tendency to enter a powerful role with probability p, and there are N members of this group, then the shifts in power distribution will have standard deviation (in percentage terms) of 1/sqrt(Np(1-p)).
That doesn't seem to agree with your "constant shift in power distribution" at all.
Also, I fail to see how your formula is meaningful at all, as it has nothing to do with power dynamics. At best, it describes the distribution of the number of powerful people in a random sample. Well, OK, how is that helpful? It cannot describe any shifts in power as it assumes independence, where our understanding of power is anything but (you are more likely to be powerful if you're close to powerful people). The actual dynamics is a collection of non-linear processes in a complex system. A very, very crude example of a somewhat similar process is that of segregation[1] with the addition of random populations during the run. It is processes with strong correlations between neighboring agents that tend to show stability pockmarked with rare bifurcations, which is exactly what we see in human society.
When I went to study history in graduate school, I dreamt of applying math to historical events. Playing with cellular automata to recreate certain shifts in history is fun, but eventually teaches us little, as we cannot say much more about the model than the same qualitative descriptions historians give anyway. It is sometimes cool to figure out the values of certain variables in the model and assign them meaning (like the "despair level prior to the French Revolution", but even these numbers don't tell us much because the models are so sensitive we can't be sure we got them right, and even if we did, it's virtually impossible to measure the values directly rather than figuring them out retrospectively. Therefore, speaking about events in broad qualitative terms is often the best we can do (compound cellular automata's Turing completeness with the non-linear ODEs defining the automaton's rules and the difficulty measuring variables directly and you get very little predictive ability).
This is clearly wrong - I demonstrated a stupidly simple alternate theory which disagrees with the consensus, but still lacks constant power shifts.
Rapid shifts in the composition of various fields would debunk basically every theory that presupposes human nature doesn't rapidly shift. As such, your theory proves very little, and other theories (e.g. mine) make the same predictions. So why cling to that theory, rather than, say, my theory of p=A - B x math_content + second_order_corrections?
My theory predicts more things (e.g., it predicts % women in academia, % women in finance, % women in tech vs non-tech roles) and is vastly simpler. How is that not a win?
Your theory didn't even explain the data (in the software industry), and had nothing to say about power. Basically, it can comfortably exist beside the consensus theory as a second-order effect (and the data actually looks like that is probably the case, explaining representation differences of up to 2:1).
> So why cling to that theory, rather than, say, my theory of p=A - B x math_content + second_order_corrections?
Two reasons: 1. your theory doesn't explain the anomalous software industry (neither the very low participation nor the sudden change) while the consensus theory does, and 2. your theory doesn't explain the lack of representation (and possible correction after well-documented struggles) in fields of high prestige and little math (such as law, medicine and politics). In all those fields: law, medicine, politics and software, women participation was (or is) far lower than 30%. It was/is lower than 20%.
You might think that singling out software is uninteresting from a statistical perspective, as in Scott Alexander's regression it was just a single (outlier) data point, but in fact, the software industry is larger than all "heavy math content" professions combined, and holds more power in today's society.
> My theory predicts more things (e.g., it predicts % women in academia, % women in finance, % women in tech vs non-tech roles) and is vastly simpler. How is that not a win?
Because it predicts fewer things, and not even what you claim it does. At best, it predicts fewer women than men in certain subjects, but that's it. However, we see that while the binary relation "fewer" may remain, how much fewer decreases over time. Second, it only holds (even as a binary prediction) when you look at the past few decades -- far too short to look at social change -- which means it does not explain the exclusion of women from law, medicine and politics. Third, it does not explain the way-too-low representation in CS, nor the drop in participation. The consensus theory explains all of it, for any time duration. It even explains interesting shifts we see in, say, education (more women as prestige drops, while in CS fewer women as prestige rises). Yes, it's more complicated, but fits reality better, plus it's supported by lots and lots of data.