Disagree. Mathematical objects exist in the same way physical objects do at the very least, i.e., the standard anti-solipsist arguments for the existence of the physical world apply equally well to mathematical objects.
I sort of agree, but probably not in the way you mean. In the above I followed the map/territory meme, where you can find sheep in the territory, but the numbers in the map. However, I am interested if you outline or link to the arguments you mention.
In the above I followed the map/territory meme, where you can find sheep in the territory, but the numbers in the map.
Yes, but the numbers also constitute a territory. This is similar to the way that a physical road map corresponds to a territory, but is also in the territory in the sense of being a physical object.
However, I am interested if you outline or link to the arguments you mention.
I’m not going to be able to formulate it as elegantly as Eliezer (and I don’t remember which of his posts and/or comments this is from), but the basic idea is that even if our sense data come from nothing, I want to know why the nothing seems to be so lawful. Basically the physical world exists because it displays consistent patterns in a lawful manner, the same obviously applies to mathematics.
Yes, but the numbers also constitute a territory. This is similar to the way that a physical road map corresponds to a territory, but is also in the territory in the sense of being a physical object.
Can’t say I agree that numbers are like physical representation of maps, but that would be a discussion for another day.
Basically the physical world exists because it displays consistent patterns in a lawful manner, the same obviously applies to mathematics.
I do not agree that this is an accurate map. Consider a random collection of dots: human eye can find patterns in it. Chances are, what we think of as physical laws are just the patterns we distill from the utter randomness.
Not working for me. Try imagebin or something. Also note that the compression can be very lossy. The real test is how well one can extrapolate from a small patch outward.
The issue isn’t where they’re stored. The explicit links I gave work, but they work only intermittently from within Markdown. If I load the permalink for my comment they don’t show. But if I open the two explicit links in separate windows, then reload the permalink, the Markdown links work.
It doesn’t work if you just click the link, but if you copy the link address and paste it in a browser then it works. (Because there isn’t a referrer header anymore.)
Your web server is giving a 403
Forbidden response to requests that
include a referer, which includes
(in most web browsers) requests for images in
elements. This can
probably be configured somewhere on your web server. You may currently have
something like
this
enabled and you’ll need to disable it.
(A reason someone might want this behavior is to prevent
hotlinking, but in this case,
you want to hotlink your own image.)
The reason that the behavior is intermittent is presumably caching on your
browser. When I tested it from the command
line the behavior seemed quite consistent.
I blame browser caching. In the process of testing I made several dozen requests without a Referer and all of them were 200 OK (and in the case of a couple dozen of those I double-checked that the file contents were identical with each other).
Edit: Actually, you can test this if your Apache install is set to log Referers to your access log (this is a common default). If so, you’ll probably find that the 403 lines have Referers and the 200 lines don’t. (You may also see some 304 Not Modified responses there, which would probably be either all without Referers or maybe a mixture.)
All numbers are abstractions and are therefore in the map. Positive integers have no more claim for existence than quaternions or what have you.
Disagree. Mathematical objects exist in the same way physical objects do at the very least, i.e., the standard anti-solipsist arguments for the existence of the physical world apply equally well to mathematical objects.
I sort of agree, but probably not in the way you mean. In the above I followed the map/territory meme, where you can find sheep in the territory, but the numbers in the map. However, I am interested if you outline or link to the arguments you mention.
Yes, but the numbers also constitute a territory. This is similar to the way that a physical road map corresponds to a territory, but is also in the territory in the sense of being a physical object.
I’m not going to be able to formulate it as elegantly as Eliezer (and I don’t remember which of his posts and/or comments this is from), but the basic idea is that even if our sense data come from nothing, I want to know why the nothing seems to be so lawful. Basically the physical world exists because it displays consistent patterns in a lawful manner, the same obviously applies to mathematics.
Can’t say I agree that numbers are like physical representation of maps, but that would be a discussion for another day.
I do not agree that this is an accurate map. Consider a random collection of dots: human eye can find patterns in it. Chances are, what we think of as physical laws are just the patterns we distill from the utter randomness.
Not enough to compress it substantially.
Random collection of dots:
Not a random collection of dots:
ETA: Well, those links weren’t working, then they were working, currently they aren’t. The actual URLs are http://kennaway.org.uk/images/noise.jpg and http://kennaway.org.uk/images/notnoise.jpg
ETA2: And now they’re working, or not, at random.
Not working for me. Try imagebin or something. Also note that the compression can be very lossy. The real test is how well one can extrapolate from a small patch outward.
The issue isn’t where they’re stored. The explicit links I gave work, but they work only intermittently from within Markdown. If I load the permalink for my comment they don’t show. But if I open the two explicit links in separate windows, then reload the permalink, the Markdown links work.
If I click on the links it just says “Forbidden”. Perhaps they work for you because you have access permissions that we don’t?
The site doesn’t know who I am when I access them. They work for me from anywhere. Is there anyone else they do work for?
The explicit links weren’t working for me.
It doesn’t work if you just click the link, but if you copy the link address and paste it in a browser then it works. (Because there isn’t a referrer header anymore.)
Your web server is giving a 403 Forbidden response to requests that include a referer, which includes (in most web browsers) requests for images in
(A reason someone might want this behavior is to prevent hotlinking, but in this case, you want to hotlink your own image.)
The reason that the behavior is intermittent is presumably caching on your browser. When I tested it from the command line the behavior seemed quite consistent.
That is probably it. It doesn’t explain the direct links failing though.
I blame browser caching. In the process of testing I made several dozen requests without a Referer and all of them were 200 OK (and in the case of a couple dozen of those I double-checked that the file contents were identical with each other).
Edit: Actually, you can test this if your Apache install is set to log Referers to your access log (this is a common default). If so, you’ll probably find that the 403 lines have Referers and the 200 lines don’t. (You may also see some 304 Not Modified responses there, which would probably be either all without Referers or maybe a mixture.)
Well, clicking on the links and then reloading doesn’t work.