Asortyment Nieskończoności

Jest to prezentacja Powerpoint, prelekcji której udzieliłem w Otwartej Kolonii (filii Wolskiego Centrum Kultury) 20 kwietnia. Ten wykład to krótka historia pojęcia niskończoności, oraz wstęp do arytmetyki liczb kardynalnych poprzez prezentację dowodów Cantora na równoliczność zbiorów nieskończonych. Poniższa prezentacja zawiera trochę definicji oraz pomocy ilustracyjnych, ale oczywiście brakuje jej niezbędnej narracji która wyjaśnia wszystkie pojęcia oraz ich relacje.

Asortyment Nieskończoności PDF by Mariusz Popieluch on Scribd

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Lucid Sententia XIX

Out of the septillions of living organisms coming in and out of existence in the history of life on Earth, only a tiny fraction are those with whom we have the privilege to coexist. They are special. We are special, as a kind of temporal family.

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APP IDEAS. App idea #1: musical piece search based on crude "singing" input.

I'll start a new series of posts, where I describe various app ideas. This should be a fun exercise and it's probably a good idea to publish---the hope being that it may inspire someone. I'll begin enumerating with #1 as an indicator when I started posting those ideas---this is not meant to interpreted that #1 indicates the first app idea I've had.

App idea #1: musical piece search based on crude "singing" input.

Consider an app whereby the software recognizes the music piece from a crude rendition---sung or hummed---of one of it's fragments. I have noticed this to be most useful in the case of classical music---we often recognize the melody, but are at a loss of who composed it or what the title is. It should be useful when we want to share the piece with someone but don't know what to type into the search app. So how about just having a search app that takes crude renditions as input? There's some promising speech-recognition software out there, so perhaps implementing this idea could make us of it. 

Ad hoc theory of one of the reasons why time appears to flow faster in dreams.

A perplexing yet strangely familiar experience to anyone who has ever dreamed, would undoubtedly have been making the occasional observation that much more seems to occur in our dreams than the duration of our sleep alone can account for. After a night of intense dreaming we often remember the equivalent of much a longer time period then we had actually spent sleeping (which is generally much longer than the time spent dreaming). Or when we take a short nap during the day, we're often surprised to learn upon waking that only a few minutes have past after what had seemed like an epic adventure. 
So apparently there's a clear subjective disconnect between dream state and waking state with regard how we perceive the flow of time. I make the assumption that time doesn't actually undergo some substantial warping in our heads in a way that would account for this phenomenon.

Since we're under the impression that more has happened during our dream than the time being asleep can account for, there seem to be a few possibilities as to why that may be. I should mention that I'm writing this blog post without having consulted any particular, specialist literature on the matter, hence the post title. 
One possibility is that our brain processes inner-conjured dream-films with a higher temporal resolution. That is, the dream-films are presented to us with increased speed, but we perceive them as normal, since within our dream state there's no other reference frame other than the dream itself. This hypothesis appears to be amiable to empirical exploration.

The other possibility, which occurred to me recently, is closely related with how our memory works. So the following explanation requires both some assumptions about the mechanics of our memory, but also some assumptions about the actual content of dream-films. The vast majority of us, whenever recollecting some series of events---say our last birthday party, or the recent trip to the countryside---tends to recall vivid snapshots of the more intense impressions, which are more or less arranged in chronological order. The point is that most of us don't remember the entire experiencial continuum, but rater a collection of short vivid fragments. Now, if we think about it, this is how dreams often seem to manifest---in a bunch of , more or less, disconnected situations combined into one weird stream.

Of course when I talk about this, I have only my memory to rely on, so if our memory indeed works as I just have outlined, then I cannot justifiably rely on it to speak of the character of the dream-films. But the point is that it is possible that dreams may be arranged and have the actual content analogous to the way our memory works. That is, dreams may consist of vivid fragments connected haphazardly with a vague chronological cause-effect narrative sense, like a movie trailer. But because our memory also works, as assumed earlier, such that we tend to only recall movie-trailer-like imagery, and only infer all the in-between events that must have occurred, when presented with the dream-film trailer, we inflate its content by inferring that there must have been intervals in-between.

For example, in real life, when recalling our plane journey from one city to another, we may only vividly recall say, the departure and arrival, plus a few more interesting cloud formations viewed through the window on the way, but that doesn't mean that the journey only consisted of those few intervals (the sum of which may consist of less than a minute of vivid mnemonic imagery), because as a matter of fact the journey is much longer (say, a few hours) than the sum of our recollected and vivid fragments---we infer that there must have been in-between intervals, other than those that we can vividly access.

But it's possible that my dream of a similar flight would be a kind of film trailer actually consisting of only the vivid fragments of the departure, a view of the more interesting cloud formations, and the arrival, arranged in a sequence of one vivid fragment occurring immediately after the previous one, without any intervals in-between at all. However upon recalling this 3-scene act when we wake up, it seems much longer because our memory mechanism inflates this vividly dreamed sequence by filling it with inferential content, i.e. a journey like that must have lasted a few hours (there must have been many more scenes in this act).

So the ad hoc explanation of why time appears to flow faster in dreams is that dreams are much like film trailers, but because of how our memory works, we tend to have the impression that we've watched the entire film.

I've also written about about how our memory works in a recent post, and a short story written years ago.

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