All of ellenjanuary's Comments + Replies

Elaborating on Davis's remarks: what you have to consider is that mathematics is something of a game, something of an art, and something of a science - to become a mathematician is not to be declared such, but to develop the skill of mathematics. On the point of zero: just to begin with, consider subtraction. Subtraction is a simple operation, the inversion of addition - because one plus one is two, two minus one is one. When we consider this operation, we discover that there is nothing to prevent us from subtracting a number from itself unless we make a rule such - and why should we? The only reason to make such a rule is to appease an idea of numbers which does not include those less than zero, and that is no reason at all. So, we call this number - one less than one, two less than two, etc. - zero. We find it behaves as the other numbers do - it may be added, subtracted, multiplied just as other numbers, and that it cannot be divided by suggests a host of new ideas. Calling zero a number pays dividends. Therefore zero is a number. Quod erat demonstrandum.

Your passion is admirable, but you would seem to have much more to learn before you are ready to make your greatest contribution. (As do we all, of course.) For instance, the mathematical community at large actually does consider zero to be a number; this is not really in contention. Here at Less Wrong, we prefer focused, previously-researched posts: probably this partially explains the downvotes you've been getting. Have you considered getting your own blog? Keep studying, and I hope to see your work in the future.

I apologize for the belated reply, but did you sincerely believe this at the time at which you said it, and do you sincerely believe it now?

Being an artist has nothing to do with the accuracy of this belief. There are two problems here. First, irrational numbers are the ones that cannot be expressed as a fraction of integers. Transendentals are defined as numbers that are not algebraic. All transcendental numbers are irrational, but the converse does not hold. Second, pi is defined as the ratio of circumference to diameter, true. This would only be a contradiction if both the circumference and diameter could be integers at the same time, which is impossible. You are confused about what numbers actually are. Some classes of numbers are useful for certain tasks, but there is no sense in which one class is more 'real' than another. I recommend Mathematics, Queen & Servant of Science by Eric Temple Bell for a wonderful overview of mathematics. Chapter 2, "Mathematical Truth", is relevent to this discussion. Also, see Godel, Escher, Bach, Chapter 11: "Meaning and Form in Mathematics".

Forgive me for stealing the gusto of your post, but it seems I can't make a comment on an old post. I am new here, and I can't help but think that some things are being over looked here. ---------------------------------------- Maybe everyone is already thinking this, so everyone feels that no one needs to say it (but isn't that exactly the "problem" this is discussing). I absolutely disagree that generalizing from one example is a bad thing. I do agree that people tend to make that idea permanent, rather than just taking it as a starting point. We are human. We are living, remember, reactional beings. We are able to make quick decision because we are able to come to quick conclusions. Let me give you an example. You see someone pick up a mushroom, eat it, and then die. What do you think? "If I eat that mushroom, then I will die to." But isn't that exactly the problem you discussed? Generalizing based on one example? So then you go on to do science and prove that this particular mushroom is bad and not ALL mushrooms; you find out that some (not all) people have allergies to some (not all) mushrooms; but in the mean time you were spared from trial by fire. It is important for people to be able to make a snap decision, it is important for them to be able to figure out what is "going on" from very limit examples. The problem is that people are stubborn; once a person makes up their mind, they stick to it so stead-fast, it takes extra-ordinary measures to change their mind - something like a 95% confidence at minimum (I jest). Sorry if the explanation is hard to follow. I am bad a setting up / introducing my ideas, so my meaning tends to get lost. Let me reiterate: You speak as though generalizing is bad. I disagree. You need to have a basis to get started from. You need to be able to start making intelligent decision about the world around you based on what you see. But, you cannot assume that a) you are right or b) that you have accounted for all the variables.