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You could totally do this. We tend to deal numbers by turning them into symbol sequences and then applying grammatical rules to them --- we're good at grammar,

You could totally do this. We tend to deal numbers by turning them into symbol sequences and then applying grammatical rules to them --- we're good at grammar, we have hardware acceleration for it. Digital computers work the same way: the quantity is measured, turned into a number, turned into a symbol sequence, then we manipulate those symbols before turning them back into a number. But analogue computers work by taking a measurement, representing it directly as a potential, and then performing various analogue operations on that potential to yield another potential. At no point during the operation is the potential converted to a number. (Disclaimer: our analogue computers do use numbers for I/O, because they measure the result potential and express it in ways we can understand, but that's just a UI issue.) So I can totally imagine an alien technology that manipulated quantities using mathematical operations without having any way to express those quantities themselves other than in relation to other quantities. They could use symbol streams to represent the relationships --- if so, they'd probably get on quite well with algebra --- but the idea of representing the potentials themselves as a power series would be completely alien to them.

Udik 10y ago
There are very good reasons for which we aren't typing these comments on analog computers, and we don't have analog computers in our pockets, and all the data we store, including everything that we experience as analog (music, images, video) are actually stored in digital format. And before that, the way we write language, numbers, and music is digital, not analog- despite the fact that we seem to think more in an analog way than a digital one. Come to think of it, even our language is digital, despite the fact that our experiences are not and we often struggle to find the combination of words that will better reproduce the meaning we have in our minds. Come on, this is HN, how can you not see the advantage of calculating with numbers, and writing down numbers, in place of approximate quantities? And why we converted an entire century's worth of audio and photographic recordings to a digital format?
- david-given 10y ago
  Yes --- we do that because we are symbolic creatures. We serialise thoughts into sequences of symbols so that we can express them tonally, in series, to other people. We express mathematical concepts the same way. Naturally, the machines we built to help us do these things also work symbolically. Machines built by people who think differently will work differently.
  - Udik 10y ago
    First, no, we use digital machines because manipulating analog quantities is an impossible mess. The essence of an analog quantity is that it is unquantified, and therefore there is no real way of telling if two quantities are the same or not, or whether they would have been the same if one of the two hadn't been perturbed by something. Whenever you write down (or emit in any way) analog information, you're losing part of it; it can and will be altered by any amount of noise, and altered again when it's picked up by a reader or receiver. Not altered as in "a bit of noise but we can discard that". Altered in the sense of "it's impossible to tell the information from the noise". There is not much processing or storing you can do with it. As for the fact we're "symbolic creatures", perhaps we are, but again- is it because our brains are natively digital or because we really put a lot of effort in trying to be symbolic? (I don't know whether our brains can be called digital- neural networks seem more analog than digital, but there might be quantization going on at some levels to manage the complexity and the noise of handling analog information.) Maybe symbolic reasoning emerges despite being really hard to master, because it actually manages to grasp some fundamental aspect of reality?
    - TuringTest 10y ago
      You may need to quantize data for error correction (as in "a trigger that differentiates symbol A from symbol B"), but you don't need numbers for that (as in "an arbitrary chaining of the sequence operator", which is the base of natural numbers). You can have logic -binary or not- to define rules of inference, without defining a particular rule of inference for numbers (measuring quantities). As someone else sort of implied elsewhere [1], if aliens use mathematics at all, it would probably be easier to reason with them in terms of topology rather than number theory. [1] https://news.ycombinator.com/item?id=13969500 https://news.ycombinator.com/item?id=13969500
- mcguire 10y ago
  I think quantum computing may want a word with you.

Udik 10y ago

There are very good reasons for which we aren't typing these comments on analog computers, and we don't have analog computers in our pockets, and all the data we store, including everything that we experience as analog (music, images, video) are actually stored in digital format. And before that, the way we write language, numbers, and music is digital, not analog- despite the fact that we seem to think more in an analog way than a digital one. Come to think of it, even our language is digital, despite the fact that our experiences are not and we often struggle to find the combination of words that will better reproduce the meaning we have in our minds. Come on, this is HN, how can you not see the advantage of calculating with numbers, and writing down numbers, in place of approximate quantities? And why we converted an entire century's worth of audio and photographic recordings to a digital format?

david-given 10y ago
Yes --- we do that because we are symbolic creatures. We serialise thoughts into sequences of symbols so that we can express them tonally, in series, to other people. We express mathematical concepts the same way. Naturally, the machines we built to help us do these things also work symbolically. Machines built by people who think differently will work differently.
- Udik 10y ago
  First, no, we use digital machines because manipulating analog quantities is an impossible mess. The essence of an analog quantity is that it is unquantified, and therefore there is no real way of telling if two quantities are the same or not, or whether they would have been the same if one of the two hadn't been perturbed by something. Whenever you write down (or emit in any way) analog information, you're losing part of it; it can and will be altered by any amount of noise, and altered again when it's picked up by a reader or receiver. Not altered as in "a bit of noise but we can discard that". Altered in the sense of "it's impossible to tell the information from the noise". There is not much processing or storing you can do with it. As for the fact we're "symbolic creatures", perhaps we are, but again- is it because our brains are natively digital or because we really put a lot of effort in trying to be symbolic? (I don't know whether our brains can be called digital- neural networks seem more analog than digital, but there might be quantization going on at some levels to manage the complexity and the noise of handling analog information.) Maybe symbolic reasoning emerges despite being really hard to master, because it actually manages to grasp some fundamental aspect of reality?
  - TuringTest 10y ago
    You may need to quantize data for error correction (as in "a trigger that differentiates symbol A from symbol B"), but you don't need numbers for that (as in "an arbitrary chaining of the sequence operator", which is the base of natural numbers). You can have logic -binary or not- to define rules of inference, without defining a particular rule of inference for numbers (measuring quantities). As someone else sort of implied elsewhere [1], if aliens use mathematics at all, it would probably be easier to reason with them in terms of topology rather than number theory. [1] https://news.ycombinator.com/item?id=13969500 https://news.ycombinator.com/item?id=13969500
mcguire 10y ago
I think quantum computing may want a word with you.