That's not true unless the distribution is uniform. If it were always true, then compression would not work. Compression, in a simple case, often compresses data stored as byte sized chunks into smaller space, precisely because those 8 bit integers do not have 8 bits of entropy each.
Hmm, how many bits has the space of all positive integers?
That's not what the (clumsily written) article is about. It's not about sampling the integers to choose an integer, it's about sampling the prime factors of an integer, as a measure of evenness of distribution of prime factors.
It's measuring the information in the prime factorization, the information in the number as a value.
Having ripcorded out after realizing the author was trying to prove that water was wet, I'll assume that it's "normalized entropy", in a range of 0-1, indicative of the distribution across the space.
True, but HSBC thinks you read the email, because somebody fetched the tracking pixel, right? The irony is that HSBC and others who use this kind of thing probably aren't in the least interested in when or how many times you open the email. Whoever came up with this idea (probably) really did think it was (just) a pretty good way of figuring out if they have your correct email.
Bob isn't giving you any actionable information. If Alice and Bob agree, you're more confident than you were before, but you're still going to be trusting Alice. If they disagree you're down to 50% confidence, but you still might as well trust Alice.
To complete the circle, now that we have winnowed the space down to these options, we would normalize them and end up with 0.16 / (0.16 + 0.16) = 0.5 = 50% in both cases.
The reason I'm not putting % signs on there is that, until we normalize, those are measures and not probabilities. What that means is that an events which has a 16% chance of happening in the entire universe of possibility has a "area" or "volume" (the strictly correct term being measure) of 0.16. Once we zoom in to a smaller subset of events, it no longer has a probability of 16% but the measure remains unchanged.
In this previous comment I gave a longer explanation of the intuition behind measure theory and linked to some resources on YouTube.
In the US they don't hang it on trees, they just leave by the side of the trail or road or whatever. But it is very common to see bags of dogshit on the sidewalk or by the side of a trail in the US.
I have fun, but I probably wouldn't if the AI was right all the time. Or if I was helpless when it was wrong. But for now I'm still in the centaur zone.
if you read the article instead of just criticizing the headline:
> They listened to Michigan Attorney General Dana Nessel criticizing the lack of transparency with DTE, the utility that's associated with the Saline Township proposal, and legislators who protested tax breaks for data center projects.
> ...
> "We're talking about 1.4 gigawatts, which is, of course, enough to provide energy to a city of a million people," Nessel said. "I think we should be taking this extremely seriously, don't you? Do you guys trust DTE? Do you trust Open AI? Do we trust Oracle to look out for our best interests here in Michigan?"
this wasn't just a random group of 100 people, they were organized enough to get the state AG as well as multiple state legislators to speak. seems fairly newsworthy to me.
In Lansing, it was below freezing and windy most of the day. If I noticed 100 people standing around on the pavement for hours in that, I'd probably imagine they deserved at least some regard for their concerns. But then, I'm not a Michigan politician that needs to get gamer Johnny out of my basement and on to a cushy non-profit no-show kickback job, courtesy of whatever big tech outfit wants a data center.
It’s not just this group. A co-worker of mine went to his town meeting about a proposed data center. When he showed up it was standing room only and they had to move the meeting to a bigger venue. I’ve heard stories like this from a few people now around Michigan where they have been trying to put data centers. No one wants them.
The threshold is an organization organizing it. Getting 100 people out demonstrates your political power to your supporters and the people you seek to influence. Getting 1,000 people demonstrates that you have more of it.
There is very little common space in Michigan. There is a lot of private land, and a lot of public land, but very few spaces where people congregate. So when they do, it stands out quite a bit.
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