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[In Finnish] Voiko maailmankaikkeutemme sittenkin olla simulaatio?

[Briefly in English: No, recent result in quantum physics do not prove that we aren’t in a simulation]

Tänään ilmestyneessä tekniikanmaailma.fi:n artikkelissa väitettiin, että löydetty “kvantti-ilmiö todisti: Me emme elä jonkun simuloimassa Matrixissä”. Tosin tekstin puolivälissä todetaan, että “Asiaa ei voi tietenkään todistaa”… hetkinen, todistettiinko se vai ei? No itse asiassa ei. Kyseessä on ennemminkin rikkinäinen puhelin, jossa, uskallan olettaa, tekniikanmaailma muokkasi jo valmiiksi tieteelliset yksityiskohdat sivuavaa EurekaAlertin populaaria artikkelia. Ensinnäkin palautetaan mieleen, että alkuperäisen artikkelin abstratkissa lukee “The answer to the question—whether there is a fundamental obstruction to such a sign-free representation in generic quantum systems—remains unclear.”, eli kyseinen laskettavuuteen liittyvä ongelma ei ole edes kokonaan ratkaistu. Mutta vaikka olisi, ja jonkin asian simuloiminen ei onnistu meidän nykyisillä tietokoneillamme, ei se tarkoita sitä, ettei se onnistuisi (a) tulevaisuuden tietokoneilla (b) kvanttitietokoneilla (c) toisen universumin, toisenlaisen fysiikan lakeja noudattavilla, tietokoneilla. On kuviteltavissa argumentteja, joiden mukaan jopa tulevaisuuden tietokoneet – niin kauan kuin ne on Turing-tietokoneita, niin kuin kaikki meidän tietokoneemme ovat – eivät koskaan pysyisi reaaliajassa simloimaan universumimme osia. Tämä johtuu siitä, että ei-Turing-laskettavia funktioita ei pysty laskemaan Turingin koneilla. Jos taas kyse on vain eksponentiaalisesta kasvusta, niin kuin artikkelissa mainitaan (tosin siellä kuvaillaan eksponentiaalinen kasvu väärin: eksponentiaalinen kasvu on sitä, että yhden hiukkasen lisääminen tuplaa simulaation tarvitsemaa tehoa, eikä sitä että hiukkasten tuplaaminen tuplaisi simulaation tehoa, mikä olisi linaarinen kasvu), niin sen voi simuloida Turingin koneella – ei vain reaaliajassa. Mutta jos me olemme simulaation sisällä, niin meidän aikamme on sidottu simulaatioon, joten emme voi tietää kauan meidän universumimme yhden sekunnin simuloimiseksi menee siellä toisessa universumissa, jossa tätä simulaatiota ajetaan. Puhumattakaan siitä, että se mikä onnistuu eksponentiaalisessa ajassa Turingin koneilla, onnistuu usein lineaarisessa ajassa kvanttitietokoneilla, koska niillä pystyy (usein) ratkaisemaan P=NP ongelman. Mutta kun tullaan kohtaan (c), niin viimeisetkin argumentit kaatuvat. Katsotaan mitä niitä olikaan:

“Simulaation monimutkaisuus puolestaan kasvattaa muun muassa sen edellyttämän muistin ja sähkön määrää.”

Rinnakkaisuniversumin älykäs sivilisaatio käyttää tietokoneissaan…. sähköä? Ei välttämättä. Ja riippumatta siitä, mitä resursseja ne siihen käyttävät, emme voi tietää skaalaa, jossa toinen maailmankaikkeus operoi. Voi olla esimerkiksi niin, että sivilisaatiolla, joka ajaa tätä simulaatiota, on käytössään 17000:n mustan aukon energia. Tai voi olla, että yhden sekunnin simuloiminen vie 100 miljoonaa vuotta (joka on simuloivan sivilisaatiomme mielestä yhtä pitkä kuin 1 sekunti on meidän mielestämme). Voi olla että he ovat keksineet tavan matkustaa ajassa taaksepäin tai ehkä heidän universumissaan aika on kompleksista (eikä reaalista), eikä heillä ole mitään resurssipulaa kun kyseessä on informaationkäsittely. Voi myös olla että he simuloivat hiukkasia vain sitä mukaa kuin me näemme niitä ja sen takia kvanttimekaniikan mallissamme “havaitsijan” roolista on tullut niin poleeminen. Nämä ovat vain esimerkkejä siitä, että ainoastaan mielikuvitus on rajana sille, mitkä asiaintilat voivat pitää paikkansa.

“[I]hmiseltä [on] hyvin itsekeskeistä olettaa, että jokin korkeampi sivilisaatio tekisi simulaation juuri ihmisten kaltaisista olennoista. Ei ole hänen mukaansa kovin todennäköistä, jokin korkeampi sivilisaatio näkisi nimenomaan ihmiset simuloinnin arvoisina.”

Jos jokin sivilisaatio simuloi koko universumia, ei ole mitään syytä olettaa, että se tekee sen simuloidaakseen ihmisiä. Planeetamme on vain yksi heidän simulaationsa osa, eivätkä he ole välttämättä edes huomanneet, että yhdelle planeetalle sattui syntymään elämää tai ihmisiä. Paitsi että saatamme olla simulaatiossa, saatamme itse asiassa olla simulaation tahaton sivutuote.

Käytännössä tutkimus viittaa siihen, että on mahdotonta mallintaa nykyfysiikkaa edes tehokkaimmalla tunnetulla tietokoneella, mikä puolestaan tarkoittaa, että todellisuus ei voi olla simulaatiota.

Oleellisesti jo vastasinkin tähän, mutta siis haloo. Jos jotain ei voi mallintaa tehokkaimilla tunnetuilla tietokoneilla, mitä tekemistä sillä on sen kanssa voiko sen simuloida superälykkään intergalaktisen sivilisaation tietokoneilla? Meidän tietokoneillamme ei pysty edes luotettavasti simuloimaan Newtonin mekaniikan kolmen kappaleen ongelmaa saati viiden tai kuuden kappaleen ongelmaa, joten se ei ole mikään uutinen, että nykyfysiikkaa ei pysty simuloimaan (meidän) tietokoneillamme.

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Needy Researchers Put Academy on a Pedestal

Here is what male seduction masters teach their students: don’t be needy and don’t put the woman on a pedestal. And yes, I am comparing researcher applying for grants to men hitting on women.

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From Mathematics to Art: an interview with Tuomas Tuomiranta

Mathematicians know that mathematics is beautiful, but they have hard time explaining to others why is it so. In fact, most of the time they give up on this task. My friend Tuomas Tuomiranta hasn’t. I met Tuomas at the University of Helsinki when we both studied mathematics around 10 years ago. Several years later it came to me as a surprise to find out that he became a visual artist! In 2010 Tuomas had created simulations of liquid dynamics based on the Navier-Stoke’s and turned them into artistic animations. Another one was based on the theory of conformal mappings in the complex plane – a common topic at the University of Helsinki. Some links:

Tuomas Tuomiranta was Read more

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What is artificial intelligence today?

I was invited to give a presentation to a group of politicians, some of which are members of Finnish Parliament, today, at the Finnish Parliament Annex building (Pikkuparlamentti). Here is my visitor’s batch:

Visitor’s batch to the Finnish Parliament

My job was to inform them about what artificial intelligence Read more

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Mathemat-ART-ical Fract-ART Augumented with Deep Learning

I am fascinated by the combinations of mathematics and art for several reasons; one reason is that it is so difficult to show the beauty of mathematics to non-experts. As a mathematician I am often frustrated that my work cannot be understood by many people that are important to me. Using mathematics to create Read more

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An Interactive Animation Visualising a Group Isomorphism

An interactive animation programmed in JavaScript illustrating the isomorphism from the quotient of the additive groups of reals by intergers Latex formula to the unit circle on the complex plane Latex formula defined by the formula:

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Ozora lecture submission

I submitted a proposal for a lecture to the Ozora festival. The lecture is supposed to cover the ways in which the contemporary cognitive science is able to tackle age old questions in the philosophy of mind. The exact content of the lecture is not yet fixed, but the range of topics includes:

  • What does cognitive science have to say about the Platonism/non-Platonism debate, i.e. do abstract concepts, such as mathematical ones, posses existence independent of humans or cognitive systems in general?
  • What can neuroscience tell us about the nature of experience, meaning and consciousness? Is having a powerful enough fMRI brain scanning techniques enough to understand the relationship between the mind and the body? Even if not, how can it help?
  • What is the enactivist-representationalist debate in the philosophy of mind and cognitive science, and how is it related to meditation, embodiment, even Buddhism and spirituality?
  • How can artificial intelligence, in particular artificial neural networks illuminate our understanding of meaning, emergence and consciousness? What are the limitations and the possibilities of the present day AI systems? What is the moral and ethical side of developing thinking (and feeling?) machines?

An inspirational animation with text from Rosch, E., Varela, F., & Thompson, E. (1991). The embodied mind. Cognitive Science and Human Experience:

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More on my Algebra teaching

What tricks do you use in your teaching or have found useful while studying? Comment below!

A couple of months ago I wrote about my eccentric first algebra lecture. I am lecturing Algebra I in this semester which is in fact split into two parts. The teaching methodology this course is being taught in (and has been taught a couple years before me) is already of interest to people outside of our department. I have additionally experimented with some extra stuff such as magic tricks and YouTube videos and below I summarise all that.

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Cognitive Science of Philosophy of Mathematics – workshop

Short motivation

What is mathematics? How is mathematics produced, understood and learned by the human brain? Do infinities exist or are they a product of our minds? Whether or not they exist, mathematicians’ minds can conceptualise infinity. What does this mean and how is this possible? Is mathematics limited and shaped by human brain and body or is it completely independent of the agent doing it? Would extraterrestrial aliens have the same mathematics as we do?

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The Kick-ass Value of Expert Advice

New: Don’t have time to read? Scroll down to watch a 1-minute summarising video instead.

Last Tuesday I was, as regularly, practising acrobatics in Sirkus Huima’s free exercise shift. Osmo Tammisalo who is, among other things, an expert acrobat happened to be there and he came to watch my back flip. He started giving me some advice and in the first ten minutes my back flip improved more than in the previous two months. After these ten minutes he said “perhaps it will help if you learn flic-flac first”. I was horrified. Flic-flac? I always thought it was extremely difficult, and considered it much more difficult and scarier than the back flip. But he insisted that I try to jump backwards… even if landing on my head (don’t worry, into a sea of pillows). And so I did. After 15 minutes of practice under his supervision, this was the result (video):

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Representation and Enactivism

Think of a place that you visit often but where you are not located right now. Maybe it’s your kitchen or your bedroom.  Imagine that you are walking around that place. For simplicity I  will assume that it is your kitchen. You can ‘see’ where the stove and the fridge are, where the window is and so on, can’t you? Maybe you can even navigate in your imaginary kitchen and you can add things to your imaginary experience that are not normally there: A lion in your kitchen? A monster under the table? A gazelle in your fridge? Or who knows, maybe you have one.  Does this ability of yours mean that you have a representation of your kitchen in your brain?

In this blog post I will explore a philosophical debate between philosophers of mind who claim you have and those who say that no, you haven’t. There are two partial solutions that I will present. One is based on resolving some apparent contradictions showing that many things are actually either compatible with both views or just results of misconceptions. The other is based on the distinction between the two notions of information: semantic and non-semantic.

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Bees vs Penguins

Look at these photos:

Left: By Waugsberg from https://www.phactual.com/springtime-is-here-and-so-are-the-bees/ Right: Original: Stan Shebs, Both licensed by Creative Commons Attribution-Share Alike 3.0 Unported License

The size of the wing of a bee in proportion to her body size seems to be virtually identical to that of a penguin. The length of the wing in both animals is around half their height. Why does the bee fly effortlessly while the penguin has absolutely no chance of even slowing down his free fall to save his life? If you read my earlier post about giant grasshoppers, you probably guess the answer…

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Working in solitude, guiding students to find themselves, and thoughts on the modern academic world

Wolf Singer and I

Wolf Singer (right) and I

 

In Vienna I had the opportunity to quickly interview Professor Wolf Singer. He is a Senior Fellow at the Ernst Strüngmann Institute for Neuroscience in Frankfurt, Germany, that he has founded in cooperation with the Max Planck Society a couple of years ago. One of the most fascinating ideas around which the modern work of Wolf Singer and his colleagues focuses is that brain performs a form of liquid computing. Imagine a pool of water. If you drop a small stone in it, waves will propagate in every direction. All the particles of the water body start moving – but in a predictable way. Suppose you drop two stones at different points simultaneously. The wave pattern will become more complicated. Some waves will cancel each other out, some will amplify each other. These waves can be thought of performing some sort of coding of the “inputs” (the stones) that the system has received. We know from EEG data that the brain is constantly performing rapid wave-like fluctuations. The idea behind liquid computing in the brain is that these waves measured in EEG are akin to waves in a liquid container. The brain’s activity is fluctuating and the complex fluctuations are thought to represent the superposition of the priors, i.e. the a priory knowledge, needed for the interpretation of sensory signals. Once sensory data are received, some waves get amplified, others diminished and this corresponds to a kind of a collapse of the matching priors to the actual perception. Wolf Singer acknowledged that there is a certain similarity to quantum mechanics. He even said that nature, by evolving the cerebral cortex, perhaps figured out the closest possible way of imitating principles of quantum computing within a classical system.

Between his lectures in Vienna I had a quick opportunity to interview Wolf Singer about his working patterns and habits.

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London-Vienna-Seville-Barcelona-Pucon

I had an exceptional amount of travel in the last couple of months. My first destination was London and I want to mention the exhibition “Colour and Vision” they have at the Natural History Museum in South Kensington – it is still open for several weeks, until November 6th. I went there with my friend’s four year old son while my friend was at work. Read more

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On Lord’s and Other Prayers

My friend Sam recently asked me what do I think of Lord’s Prayer and I decided to publish my response here. Since I didn’t grow up religious and was never particularly keen on praying, this was the first time I was actually exposed to the content of this prayer. This makes me somewhat unbiased compared to someone who had to repeat it multiple times in childhood.

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