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The largest number representable in 64 bits

tromp.github.io

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Re: The largest number representable in 64 bits

#61

Post by b65e8bee43c2ed0 »

tdb7893 wrote: post #48
tromp wrote: post #32

Please no more comments to the extent of "i can define a much larger number in only 1 bit". What makes my blog post (hopefully) interesting is that I consider tiny programs for computing huge numbers in non-cheating languages, that are not specifically equipped for doing so.

So HN can't do this because I don't think it tracks all clicks but I've been of the opinion for a while that most social media should have the option for posts to not allow people to comment unless they've actually clicked on the link.

like the rest of simple solutions to complex problems suggested by otherwise (seemingly) intelligent people on HN, it simply wouldn't work. do you really not see why?

Re: The largest number representable in 64 bits

#65

Post by tdb7893 »

b65e8bee43c2ed0 wrote: post #61
tdb7893 wrote: post #48

Earlier quoted context omitted.

So HN can't do this because I don't think it tracks all clicks but I've been of the opinion for a while that most social media should have the option for posts to not allow people to comment unless they've actually clicked on the link.

like the rest of simple solutions to complex problems suggested by otherwise (seemingly) intelligent people on HN, it simply wouldn't work. do you really not see why?

Are you talking about that people could just click on the link then not actually read it? The thing is that clicking on the link then closing is serves as both a slight barrier to entry targeted at the people who comment without reading and also a reminder that there is an actual article to comment on. It's not going to fix discourse but the theory behind it is to be a slight nudge to get people who don't click to at least consider reading the article (or just not comment) while being an invisible change to people who actually read the article. It's not meant to be a magic fix, it's just some something I would want (though I'm biased since I click on links so there's no downside to me).

Re: The largest number representable in 64 bits

#66

Post by deathanatos »

abcde666777 wrote: post #59

Hi guys, I've come up with a new 64 bit number representation where 0xFFFFFFFF is infinity. Hell you know what every value is just infinity.

Assuming your representation's infinity is size of ℵ₀, I set my representation's 0xFFFF_FFFF to the size of ℵ₁. Similarly, if you choose ℵ_(n), I'm choosing ℵ_(n+1).

Re: The largest number representable in 64 bits

#67

Post by ShroudedNight »

tdb7893 wrote: post #65
b65e8bee43c2ed0 wrote: post #61

Earlier quoted context omitted.

like the rest of simple solutions to complex problems suggested by otherwise (seemingly) intelligent people on HN, it simply wouldn't work. do you really not see why?

Are you talking about that people could just click on the link then not actually read it? The thing is that clicking on the link then closing is serves as both a slight barrier to entry targeted at the people who comment without reading and also a reminder that there is an actual article to comment on. It's not going to fix discourse but the theory behind it is to be a slight nudge to get people who don't click to at…

Wouldn't browser prefetching subvert these small frictions to entry?

Re: The largest number representable in 64 bits

#68

Post by leodavi »

To the author: this work you've published rests on some background knowledge that I'm familiar with but also a lot of background knowledge that's foreign to me. For the parts I was able to follow, I thought the mental gear-turning was enjoyable and interesting! But pursuing these intersections between algebra and computer science is often not so interesting, at least, when I research it myself. Is this something you've learned in university? I ask because I fear that without a formal learning environment, I may never pick up on the more advanced logic halfway through the article. Anyway, cheers to the good work.

Re: The largest number representable in 64 bits

#69

Post by deathanatos »

tromp wrote: post #32

Please no more comments to the extent of "i can define a much larger number in only 1 bit". What makes my blog post (hopefully) interesting is that I consider tiny programs for computing huge numbers in non-cheating languages, that are not specifically equipped for doing so.

Which is what makes the headline bait. We start with "The largest number representable in 64 bits" (which obviously depends on the representation, and as the baited comments point out, if that's freely settable, we can just set it arbitrarily high). But the body then moves the goalposts to "using a Turning machine", "using a Turing machine with specific parameters fixed", to "lambda calculus", etc.

This is now (at least) "The largest number representable by a Turning machine of fixed parameters that can then be squeezed into 64 bit."

(I don't remember my lambda calc, so … eh.)

Re: The largest number representable in 64 bits

#70

Post by drob518 »

In a sense, this is just an exercise in (possibly lossy) compression. 64-bit unsigned into are not lossy. 64-bit floating point is lossy but has larger range; it’s only able to encode a small fraction of the numbers in its range (in the limit, the fraction that can be represented is zero since there are infinite real numbers in the range and FP only captures a few).
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