After six months of blogging nearly every weekday, I’m taking a four day weekend. This will give you a chance to browse through the archives for all the good stuff you might have missed. Or, if you’re looking for a good read to tide you over, I can recommend Chapter Two of my book Fair Play. Some of the examples are dated (Wal-Mart, as far as I know, no longer advertises that “we buy American so you can too”), but it makes a good companion piece to yesterday’s post.
I’ll be back on Tuesday with, I expect, something new to say.
let the furious wumpus commence! ;]
i for one would like to take this moment to try and present another arguement against the idea that math is discovered and not created.
on my desk i have one pencil and two paper clips.
one is as archetypical of a term as pencil. the pencil could be either brand new or a ground down stub and still be one pencil.
the paper clips are most certainly of different dimension yet the term two would seem to imply that they are equal to each other.
enjoy your break doc! ;]
I’m enjoying your blog posts, so checked out your Kindle books on Amazon. Sadly, they all now cost more than $10, thereby ensuring that in the current hard times, I’ll instead read them in my local library.
Perhaps you could explain to your publisher that suddenly raising prices by 50% during the onset of a possible second Great Depression may not be a winning strategy.
Dave, I don’t understand your argument at all. How do objects on your desk make you think that math is created? Maybe I’m just too dense to see it, so please close the loop for me. The last sentence of your argument should be something like “therefore math is created, not discovered”.
I think Dave means that the *concept* of number is created. The people who think math is created think that the discreteness of objects, like pencils, in the universe somehow means that “number” is out there to be discovered. It isn’t–it is created. “Number”, and hence mathematics, exists in the universe, but only as patterns in intelligent minds.
I meant “people who think math is discovered…”
Dave,
I think your idea doesn’t work at the atomic and subatomic level. For example, if you have a box with some neutrons in it (and nothing else), the system is entirely defined by the number on neutrons in the box. The neutrons are perfectly indentical and indistinguishable.
But the neutrons do not possess the *concept* of number. Two neutrons, two electrons and two protons are all different things, but they all possess the same “twoness”. That is the concept of number, and it is that which is created by intelligent minds, not discovered in nature.
But arithmetic is built into the fundamental nature of the system.
You can’t add half an electron to the box and observe 2.5ness. The smallest additional amount you can add is one, and it always results in “threeness” if you do so. Humans have systematized the language that we use to describe this type of phenomenon, but it is still a property of the electrons themselves.
What you are saying (I think) is that the natural numbers are “natural” because we can use them to count discrete objects that exist in the universe.
But that is not the same as saying natural numbers are discovered. Natural numbers were created when it was realized that we could use the same numbering system to count rocks, people, stars, etc.
Neil,
When I read “it was realized,” I think, “it was discovered.”
Maybe it is my own usage, but I think realizing is the same as discovering. Realizing, to me at least, is a somewhat passive thing when a truth is put together in one’s head whereas inventing is deliberately setting out to do something and forcing it to happen by using discovered features of nature. I’d never say “it was realized we could use calculators to add for us.”
are neutrons really identical?
According to the standard model and all observations, yes. All neutrons are made of two down and one up quarks.
and theres the rub. are all down quarks equal?
Yes. As far as anyone can tell from the evidence, they are identical. If they weren’t, it would mean another undiscovered flavor of quark, and that would overturn elementary particle physics as we know it. Doesn’t mean it is impossible, just very, very unlikely.
the quarks cant be identical.
neutrons beta decay to protons with a half-life of around 15 minutes.
if you started with 3 neutrons in your box, how many would you have after 15 minutes?
if the neutrons were identical, would they not decay at exactly the same time?
But they are all equally likely to decay so they are identical.
lets say left is going to decay before right.
from a mirrored frame of reference, right would decay before left.
one decays before the other and thus they are different. ;]
having gone both forward and backward in time upon this thread, i will cede any further discussion as a waste of my carbon footprint.