Wikipedia:Reference desk/Archives/Science/2021 February 23

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February 23

Can you store any arbitrarily large amount of information in a finite space?

I have a bit of paper (1 sq cm) and one corn of rice. I divide the space in any arbitrarily large nr. and when I want to store any information I put the corn in the right position. Horizontal is for the nr. proper, vertical indicates the nr. of digits. For example, for representing the number 5, I just put in on the 0.5 mark, at the bottom, to indicate 0 decimal places. If I wanted to represent a string of 1 million digits, I'll chose the appropriate slot and place the corn there. For reading the information you just have to measure the distance from the corner of the paper to the corn. What can go wrong? --Bumptump (talk) 14:04, 23 February 2021 (UTC)

The amount of information that can be contained in a given medium is a major field of study in the surprisingly named information theory. There is NOT an arbitrarily high amount of information that can be stored; indeed even space itself has a maximum amount of information that it can store owing to limits of quantum theory and the like. The problem with your system is that the corn has physical dimensions, which introduces a lower bound on the uncertainty in its position (this is normal uncertainty, not the Heisenberg uncertainty stuff that comes from Fourier transform math). At some point, using a physical device, there is always some thickness to it, and that thickness sets a lower bound on its ability to represent a distinct measurement from a nearby measurement. This isn't even getting into information theory, mind you, this is just the practicalities of working with physical objects. --Jayron32 14:21, 23 February 2021 (UTC)

"I have a ruler with an arbitrarily large number of gradations..." Matt Deres (talk) 15:35, 23 February 2021 (UTC)

Our article on this is Bekenstein bound. Graeme Bartlett (talk) 22:38, 23 February 2021 (UTC)

Somewhere before you hit the Bekenstein bound, the rice-and-paper system will run into other problems. You won't be able to arbitrarily place the grain of rice on the paper; microscopic structures on one will bump against and lock into the other. It's hard to say exactly how finely you'll be able to place the rice, but let's be extremely generous and say 1 Angstrom (10^-10 m), an atomic scale. Your square is 10^-2 m on a side. That gives you (10⁸)²=10¹⁶ choices of position in two dimensions, or only sixteen digits. Even if you could somehow position the rice to within a quantum fluctuation of a LIGO mirror, that would still only give you 36 digits. You could store more information than that by writing it with ink on the grain of rice, let alone on the piece of paper. --Amble (talk) 06:19, 24 February 2021 (UTC)

This reminds me of something I read by maybe Martin Gardner: an alien lands on earth and, being impressed with our history, decides to take a copy of the Encyclopedia Britannica home with him. He unfortunately cannot bring any extra weight back with him, but he converts every single symbol from the books into a 3-digit number and then strings them all together into a massive number encoding every single word. He then converts that into a 1/x fraction and marks that fraction very precisely on a meter stick he brought with him. The problem of course being that, no matter how rigid the stick and fine the cut there's no way you could cut it to hundreds of digits of precision, let alone the billions required for this. Matt Deres (talk) 14:54, 24 February 2021 (UTC)

If a hard drive worked by encoding all its information in the position of a single magnetic marking, a typical unit would hold about 40 bits instead of 1 TB. --Amble (talk) 17:44, 24 February 2021 (UTC)

So corrected. --Jayron32 19:16, 24 February 2021 (UTC)

It might be worth mentioning that the answers above are correct if the question is a physics question, which seems to be how it was intended. It's a very different situation if it's a mathematics question. As Matt Deres alludes to above, the position of a single point encodes infinitely much information (not just unlimited information, but actually infinite).

This is a basic fact about the real numbers, and perhaps explains why it took so long for mathematicians to develop a satisfying "rigorous" account of the reals.

It is an open question whether the real numbers are basic to the physical universe, or just an idealization that works pretty well in describing it. --Trovatore (talk) 19:32, 24 February 2021 (UTC)

Yeah, but mathematics deals with all kinds of things which aren't constrained by the physical world; there are numbers where writing out the digits in ink on paper would take more atoms than exist in the observable universe, stuff like Graham's number and TREE(3). The question did not ask about real numbers, it asked about physical objects. Once we try to remove the real constraints of physics, we enter the world of magic... and there's no point in trying to answer the question after that. --Jayron32 19:39, 24 February 2021 (UTC)

Ah, there you are quite wrong, Jayron. There's lots and lots of point in trying to answer such questions. That's what mathematicians do. If you personally don't value it, worse for you. --Trovatore (talk) 19:55, 24 February 2021 (UTC)

I think you misunderstood my response to you. When I said "The question did not ask about real numbers, it asked about physical objects", what I meant by that was "The question did not ask about real numbers, it asked about physical objects." I hope that clarifies things for you. There's lots of reasons for a mathematician to answer it. Understanding mathematics is Very Important, and we should be asking mathematical questions like this, and answering them. So, don't act like I don't believe that. I do, and you will get zero disagreement from me on that issue. Please don't tell me I don't believe that. I do. The difference is, the OP didn't ask that question. It is important for humanity to answer the mathematical questions. The answer you gave did not provide much in the way of elucidating the problem the OP presented, however, insofar as physical objects are incapable of representing the mathematics required to make an arbitrarily accurate measurement. That's the key difference. That's the issue. Mathematics is useful (in a general sense). The mathematics you're talking about is not particularly useful in answering the OP's problem. Please, in the future, if you're going to disagree with me, please disagree with the things I actually say, and don't invent something I didn't say and then disagree with that. --Jayron32 12:19, 25 February 2021 (UTC)

My first sentence in the response was It might be worth mentioning that the answers above are correct if the question is a physics question, which seems to be how it was intended. --Trovatore (talk) 19:35, 25 February 2021 (UTC)

Fair enough. It's clear I'm the asshole here. Certainly not the first time. It likely won't be the last. Sorry for that. --Jayron32 19:53, 25 February 2021 (UTC)

Perseverance's signal delay

The video feed from Perseverance's descent and landing in the ground control room looked like a live stream, but as I understand, there was a delay of a couple of minutes due to distance. So when the ground control received the confirmation of landing, does it mean that by that time the rover had already landed there several minutes ago? 212.180.235.46 (talk) 15:46, 23 February 2021 (UTC)

Yes. But it could still be a live stream. When Neil Armstrong said "The Eagle has landed", it was a couple of seconds before the people at NASA knew it. In the case of Mars, it's just a longer interval. ←Baseball Bugs ^{What's up, Doc?} carrots→ 16:00, 23 February 2021 (UTC)

Remember, everything that you have ever seen occurred some time before you saw it. EVERYTHING. Even if it happened right in front of you. It takes time for light to travel from the item or event you are looking at. It then takes time for your brain to process the input. --Khajidha (talk) 17:54, 23 February 2021 (UTC)

Are you referring to Perseverance Rover’s Descent and Touchdown on Mars (Official NASA Video) [YouTube; 3m25s]? That is a composite video. The scenes of Mission Control are taken from the live webcast of the landing on Thursday. Video of the events on Mars was recorded 11 minutes 22 seconds prior to the radio signals of those events being received on Earth, but the videos weren't transmitted until this weekend. (There is a lot of data to send, and limited bandwidth through which to do it.) The composite video was then constructed so as to synchronize the video of Mission Control reporting the status of signaled events with video of those events as they happened on Mars. So yes, the Earth portion of that video was recorded 11m22s after the corresponding Mars events happened and were recorded on Mars, but had they been able to send back live video from Mars real-time (still allowing for the 11m22s transmission time given the distance), we would have seen the same result, as Mission Control was responding to radio signals which took that same time to travel to Earth. -- ToE 21:37, 23 February 2021 (UTC)

When the New Horizons probe flew by Pluto in 2015, APL held a "live" event, counting down to and celebrating the moment the fly-by was occurring, even though Pluto was 4 light-hours and 25 light-minutes away. At one point, the live webcast cut away from the excited crowd to show the Mission Operations room ... which was totally empty as they weren't coming on duty until several hours later. See New Horizons Arrives at Pluto (YouTube; 26m11s) at 16:12 (3m45s prior to the moment of closets approach) for the shot of Mission Operations. -- ToE 22:01, 23 February 2021 (UTC)

Thanks. 212.180.235.46 (talk) 09:47, 24 February 2021 (UTC)

What's the difference between an extremely early embryo and a skin cell in terms of genetics, epigenetics, et cetera?

What's the difference between an extremely early embryo (for instance, one created through IVF) and a skin cell in terms of genetics, epigenetics, and so forth? After all, both of these things can eventually become persons--in the case of embryos, by being implanted into a fetus and in the case of skin cells, by being put in some kind of special solution and then being implanted into a uterus:

https://www.gwern.net/An-Abortion-Dialogue

Two teams of Chinese researchers working separately have reprogrammed mature skin cells of mice to an embryonic-like state and used the resulting cells to create live mouse offspring…Reprogramming has become the hottest area of stem-cell science. For more than two years, scientists have been reprogramming mature mouse- and human-skin cells and returning them to a primordial, embryonic-like state. The approach has taken off because it sidesteps the cloning and embryo-destroying techniques traditionally used to derive true embryonic stem-cell lines. However, one big question has been whether reprogrammed cells are as versatile as true embryonic cells, and whether they can form all of the cells in an embryo. Using reprogrammed cells to create live offspring with normal organs and body tissues has been considered an important test. Chinese scientists now have shown that this is possible in mice."

What exactly is it about embryos that allows them to be placed inside of a uterus immediately and then develop into actual persons whereas skin cells need to go through this additional step beforehand--as in, if skin cells are immediately placed into a uterus without actually undergoing this prior step (specifically being put in some kind of special solution), then they will obviously fail to develop into actual persons? Any thoughts on this? Futurist110 (talk) 22:12, 23 February 2021 (UTC)

Some clues are to be read in Totipotent stem cells. Embryonic cells have methyllation remove from their DNA. Graeme Bartlett (talk) 22:36, 23 February 2021 (UTC)

Is that the only distinction? Futurist110 (talk) 01:07, 25 February 2021 (UTC)