crazyjimbo

Integers can have an arbitrarily large but finite number of digits. They cannot have an infinite number of digits. There is a big difference.

Their statement makes sense: If you have a non zero probability of something happening, say P, and N times that it could happen, then you would expect it to happen about P * N times. Lets let E = P * N. Now as N goes to infinity the number of times you expect it to happen does as well. Both go to a countable infinity (Aleph 0 as you linked) which is a problem when it comes back to defining P. Normally we would say P = E / N but this doesn't make sense when E and N are both the same 'size' of infinity.

I've skimmed the paper and it's quite readable. The problem arises because probability doesn't make sense in an infinite universe. To make sense of it the authors consider a small patch of finite size and then let that finite size go arbitrarily large. In this picture probability is well defined but our space and time will always have an edge. However this is just a model, not an expected version of reality. The same thing happens in quantum field theory where the theory doesn't make sense at arbitrarily high energy so we just impose a cut off and ignore energies above a certain scale. This doesn't mean we think physics just stops there. Instead, it's just a way to parameterise our ignorance about what comes beyond.

I did a similar experiment last year. For 3 months I stuck to a low carb diet, influenced by the Atkin's diet, but not following it strictly. I was a very healthy weight and decided to try it after a number of arguments with friends and family where I defended the science behind it. I wanted to see whether it was genuinely a healthy diet, and not just the weight loss tool that it was getting all the buzz about.

I'm pleased to say the results where overwhelmingly positive. After the first unpleasant week as my body adjusted, I started to feel more energetic, less hungry and I needed less sleep. The biggest quantitative improvement though was the quality of my skin. I've always had problems with acne, even now I'm past my troubled teen years but on a low carb diet my skin almost completely cleared up. I'm sure it was more nutritious too because when you're not bulking your meals out with pasta, rice or potatoes, you don't have much choice other than to eat more veg.

After about 3 months, enough carbohydrate had crept back into my diet that I wasn't really doing anything special anymore, but I'm very tempted to go back and try to stick to it properly.

Good luck with your own experiment!

It took me far longer than it should have to get started. After clicking on the oscillator circuit I kept trying to flip the switch like your instructions say but what I didn't realise was that I had to be in simulate mode to do this. The button that makes this obvious is tucked away in the bottom left had corner - the last place I ended up looking.

Once I figured that out though I enjoyed using it.

I've looked into this problem briefly myself, and as a PhD student who runs an academically oriented start-up/web app, it's something I'd be very interested in seeing happen. In principle it should be quite easy to get working, at least for a few select journals (in my case it's the arXiv I'm interest in).

However, the one stumbling block that I see is an easy and effective way to extract citations. An important filter for whether a paper is relevant to me would be whether it cites some seminal papers in my field. There are services out there which index citations (SPIRES in my field[1]) but there is always a bit of a delay before they are updated. Using them would ruin the real-time nature of the service.

The only way I see around that is to extract the citations from the papers in the journal feed as they come in. But now the service has gone from a weekend project to a large undertaking that would require a substantial infrastructure to work.

I'll see how this thread continues to evolve, but I'd like to have further discussions about making this a reality.

[1] http://www.slac.stanford.edu/spires/

Very true, but I like my numbers to behave like... well, numbers. You can define consistent algebras but I'd argue with you if you tried to call them numbers.

It's also inconsistent if you assume that multiplication is distributive over addition:

(-1 + 1) * -1 = -1 * -1 + 1 * -1 = -1 + -1 = -2

or

(-1 + 1) * -1 = 0 * -1 = 0.

I wouldn't worry too much about what Recurly did - they seemed to constantly change their mind on how their pricing would work. Now they've given up and are holding out until to July to announce new pricing.

What I would take away from Recurly is that it can be hard to get it right first time, and changing your pricing once customers are signed up will upset some of them.

Figure out how to do the bit I don't know how to do. The rest of the application is mostly just stuff I know how to do and only need to make sure I do properly.

Figuring out how to do something is always more exciting to me than actually coding it, although normally the two can't be separated. Sometimes I need to implement a minimal framework first in order to have a setting to solve the problem.