1. Having a poor sense of direction (i.e., north, south, east, and west), potentially even with a compass.
2. Having difficulty mentally estimating the measurement of an object or distance (e.g., whether something is 10 or 20 feet away).
[And I have no idea what that "even with a compass" bit might mean. I have no more internal sense of where north is when I'm holding a compass than when I'm not, but I certainly know how to use the compass to go in whatever direction I need to go.]
The word "dysmathia," which I had been using in a tentative fashion, turned out not to work either; it's a word already in use and means a general inability to learn, which also doesn't apply to me. I have no trouble learning things -- even very complicated things like foreign languages, or very boring things I don't especially want to learn -- as long as they don't involve mathematics,
So I chose "math-numb," -- for its analogy with "color-blind" and "tone-deaf," and because for me there is an actual physical sensation associated with the problem, and I perceive that sensation as numbness. I have the same difficulty understanding and explaining why two statistical statements are different that a person who is tone-deaf has explaining why two musical intervals [pairs of musical notes] are different. If someone played two musical intervals for me and asked me to explain how they were different, and I didn't know the answer, I would know how to figure out the answer. With two statistical statements, I don't know the answer, I have no idea how I would go about figuring out the answer, and when I rummage around in my head searching for clues to the answer all I get is that sensation of numbness, as if the neurons and neuronal connections needed were either atrophied or missing.
My first memories of this problem go way back. I was in second grade, which means it was roughly 1942, and we were working on subtraction. In those days, we kids would go to the blackboard as a group to solve subtraction problems the teacher had already written on the board, go back to our desks, and then be sent to the board one at a time to explain to the teacher and the class how we had arrived at our answer.
I always had the right answers to my subtraction problems, but I never got credit for my answers. The other kids would stand at the board talking about "taking away" this and "taking away" that, and there was something they threw in now and then about "borrowing" some number or numbers, and the teacher would say things like "Very good! That's right." Me? When I was supposed to subtract 22 from 36, I would explain my answer by saying "2 and 4 are 6, and 2 and 1 are 3, so the answer is 14." And the teacher would say "Wrong! You're supposed to be subtracting!" And an extra page of subtraction problems would be added to my homework. It didn't help; to this day, I can only subtract by adding.
As for those horrible word problems where one train leaves a station at a certain time on one track and another train leaves a different station at a certain time on a different track and you're supposed to figure out when they'd pass each other .... Or those terrifying sentences like nfnitperplexity's "Though Hare is only twice as likely to win as Tortoise, his odds of winning are four times better"... Even under penalty of death, I couldn't make sense of those items.
This has been such a source of frustration to me, all my life long, that I can't even begin to describe it adequately. It has provided readers of my science fiction novels with many hilarious moments, when they spotted math errors that even young children wouldn't be likely to make. In course after course -- especially in linguistics -- I've had to find ways to work around it, and those work-arounds tend to be weird in the extreme. [Like converting all the phonemes of English on spectrograms to a set of squares on a graph, assigning the squares numerical values signifying their degree of darkness, and memorizing the set of numbers for each one, so that I'd be able to pass the final in acoustic phonetics, for example. It worked; I not only passed, I was the first person to read the spectrogram and get the correct answer. But that's truly weird.] I've managed, but I would so much rather just be able to do the math, the way other people do! I am constantly needing math skills in my work and in my research, and I am forever finding myself unable even to figure out how to ask coherent questions about what I need to know.
The one and only good thing about having grown up with this problem is that it gave me a vivid personal understanding of the situations that some of my students faced with learning disabilities of their own. I think it made me a better teacher; it certainly made me a more patient one, and more willing to listen.