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David_Gerard comments on What bothers you about Less Wrong? - Less Wrong
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I think this is a largely overestimated concept, especially on LW. I doubt most people here are "smarter" than average Joe. A lot of it is due to education, a difference of interest, and a little more ease when it comes to symbol manipulation. Surely there are many more factors, like the ability to concentrate, not getting bored too quickly, being told as a child that one can learn anything if one tries hard enough etc., but little has to do with insurmountable hardware limitations.
Eliezer Yudkowsky recently wrote:
I haven't heard of any evidence that would suggest that there are human beings who can't understand linear algebra. I myself have not yet arrived at linear algebra, because I didn't bother to learn any math when I was a teenager, but I doubt that it is something only superhuman beings can understand. I would go as far as to bet that you could teach it to someone with down syndrome.
Take for example the number 3^^^^3. Can I hold a model of 3^^^^3 objects in my memory? No. Can I visualize 3^^^^3? No. Does that mean that I am unable to fathom some of its important properties, e.g. its scope? No.
Someone who has no legs can't run faster than you. Similar differences are true about different brains, but we don't know enough about brains, or what it means to understand linear algebra, to indiscriminately claim that someone is "smarter"...
I wonder if that makes a difference in practical terms. There's all sorts of potential in one's genes, but one has the body, brain and personal history one ends up with.
What I mean is no longer feeling like the smartest person in the room and quite definitely having to put in effort to keep up.
I first encountered humans who couldn't understand basic arithmetic at university, in the bit of first-year psychology where they try to bludgeon basic statistics into people's heads. People who were clearly intelligent in other regards and not failures at life, who nevertheless literally had trouble adding two numbers with a result in the thirties. I'm still boggling 25 years later, but I was there and saw it ...
See above, but I am basically one of those people. My own intelligence lies in other areas ;-)
When I first saw a fraction, e.g. 1/4, I had real trouble to accept that it equals .25. I was like, "Uhm, why?"...when other people are like, "Okay, then by induction 2/4=.5"...it's not that I don't understand, but do not accept. Only when I learnt that .25 is a base-10 place-value notation, which really is an implicit fraction, with the denominator being a power of ten, I was beginning to accept that it works (it took a lot more actually, like understanding the concept of prime factorization etc.). Which might be a kind of stupidity, but not something that would prevent me from ever understanding mathematics.
The concept of a function is another example:
...so it goes. My guess is that many people appear stupid because their psyche can't handle apparent self-evidence very well.
If only by its effect on yourself and other people. If you taboo "smarter" and replace it with "more knowledgeable" or "large inferential distance", you do not claim that one can't reach a higher level:
"That person is smarter than you." = Just give up trying to understand, you can't reach that level by any amount of effort.
vs.
"That person is more knowledgeable than you." = Try to reduce the inferential distance by studying hard.
I believe that to be the case with literally every new math problem I encounter. Until now I have been wrong each time.
Basic arithmetic can be much harder for some people than others because some just do the logic of symbol manipulation while others go deeper by questioning axiomatic approaches. There are many reasons for why people apparently fail to understand something simple, how often can you pinpoint it to be something that can't be overcome?
Thinking about this a bit longer, I think mathematical logic is a good example that shows that their problem is unlikely to be that they are fundamentally unable to understand basic arithmetic. Logic is a "system of inference rules for mechanically discovering new true statements using known true statements." Here the emphasis is on mechanical. Is there some sort of understanding that transcends the knowledge of logical symbols and their truth values? Is arithmetic particularly more demanding in this respect?