## Friday, July 24, 2009

### Alien Mathematics

(The above sidebar text and illustration are from the New Scientist article by Martin Rees discussed below. The caption for this picture reads: An alien's description of the cosmos might teach us a thing or two about the nature of reality)
(Image: Wolcott Henry/National Geographic/Getty)

Last entry, in The Flexi-Laws of Physics, we talked about the amazing possibility that the basic "locked in" physical laws of our universe may have been retroactively adjusted during the initial stages of creation.

Back in July 2006 over at the tenth dimension forum, here's one of the discussions we got into within its very first month: our universe exists within spacetime, and space is not the same as spacetime. If we have a 3D space without time, then we can define a set of co-ordinates within that space with values for x,y, and z: but without the direction of either "time" or "anti-time" these co-ordinates can't be changed, they're locked in. These co-ordinates could then all be referenced within a planck-scale "frame" of spacetime, which we can think of as a "point" within the 4th dimension. If we move to some other different 4D point, then all three values for x,y, and z can be changed. Taking that idea to the seventh dimension, we can see that if our universe is "locked in" by a single 7D point, then there must be an unchanging set of values for u,v,w,x,y and z, which would be six arbitrary letters assigned to the six degrees of freedom afforded by the six spatial dimensions below. Which leads to the question that was discussed at the tenth dimension forum, are there six aspects of our universe that remain unchanged throughout its existence? At the time, I suggested to forum regular Daniel McQueen that there seemed to be an interesting tie-in there with astrophysicist and cosmologist Martin Rees, whose book I had read a couple of years before.

Do those six numbers really connect to the first six dimensions as I've visualized them? Is it possible to consider a wavefunction of all possible outcomes for our universe and have them all be constrained by six values, six unchanging "positions" within sixth dimensional space? That's a tricky possibility to wrap your head around. On the other hand, the idea from string theory that our universe is "locked in" at the seventh dimension by a D7 brane does seem to be a more likely connection.

Earlier this year, Sir Martin Rees published an article in New Scientist called Mathematics: The only true universal language. Let's look at the opening paragraphs of this article:
IF WE ever establish contact with intelligent aliens living on a planet around a distant star, we would expect some problems communicating with them. As we are many light years away, our signals would take many years to reach them, so there would be no scope for snappy repartee. There could be an IQ gap and the aliens might be built from quite different chemistry.

Yet there would be much common ground too. They would be made of similar atoms to us. They could trace their origins back to the big bang 13.7 billion years ago, and they would share with us the universe's future. However, the surest common culture would be mathematics.

Mathematics has been the language of science for thousands of years, and it is remarkably successful. In a famous essay, the great physicist Eugene Wigner wrote about the "unreasonable effectiveness of mathematics". Most of us resonate with the perplexity expressed by Wigner, and also with Einstein's dictum that "the most incomprehensible thing about the universe is that it is comprehensible". We marvel at the fact that the universe is not anarchic - that atoms obey the same laws in distant galaxies as in the lab. The aliens would, like us, be astonished by the patterns in our shared cosmos and by the effectiveness of mathematics in describing those patterns.
Rees then takes us through an exploration of the different mathematical breakthroughs which occurred in the twentieth century, which moves us on to superstrings as the dominant cosmological theory of our time. He mentions that despite the commercial success in the last few years of popular books claiming that string theory is "not even wrong", many of the brightest minds of our day continue to explore this promising field. Martin Rees writes:
String theory involves scales a billion billion times smaller than any we can directly probe. At the other extreme, our cosmological theories suggest that the universe is vastly more extensive than the patch we can observe with our telescopes. It may even be infinite. The domain that astronomers call "the universe" - the space, extending more than 10 billion light years around us and containing billions of galaxies, each with billions of stars, billions of planets (and maybe billions of biospheres) - could be an infinitesimal part of the totality.

There is a definite horizon to direct observations: a spherical shell around us, such that no light from beyond it has had time to reach us since the big bang. However, there is nothing physical about this horizon. If you were in the middle of an ocean, it is conceivable that the water ends just beyond your horizon - except that we know it doesn't. Likewise, there are reasons to suspect that our universe - the aftermath of our big bang - extends hugely further than we can see.
Regular readers of my blog will recognize that Martin Rees is using a similar visualization to the one I used in my blog entry "The Holographic Universe": visualizing that space-time rather than space has a very slight curvature to it allows us to see how we could be like someone floating out in the middle of an ocean, perceiving a universe of a certain size and age, but that the universe itself could be much larger than what we are able to see. Imagining, then, that an alien race billions of light years away would also find themselves to be right at the very center of an equally spherical universe of a similar age ties to the surprising idea we explored in "Where Are You?": no matter who you are or where you are in the universe, you are right at the center! Extending this idea into a set of parallel universes for our own universe, and a multiverse landscape for all other possible universes, becomes even more boggling. Martin Rees writes:
The multiverse confronts us with infinities, multiplied by other infinities - perhaps repeatedly. To bring sense to these concepts, we must deploy the mathematics of transfinite numbers, which date back to Georg Cantor in the 19th century. He showed that there was a rigorous way to discuss infinity and that in a well-defined sense there are infinities of different sizes. Without these exotic concepts, cosmologists will not be able to firm up the concept of the multiverse theory and decide, without paradoxes or ambiguities, what is probable and what is improbable within it.

The final section of Sir Martin's article gets into ideas that seem to relate to our discussions from the past month, as we looked at Computers and Consciousness, Logic vs. Intuition., and Connecting It All Together. He concludes:
Maybe in the far future, though, post-human intelligence will develop hypercomputers with the processing power to simulate living things - even entire worlds. Perhaps advanced beings could even simulate a "universe" that goes far beyond mere patterns on a checkerboard and the best movie special effects. Their simulated universe could be as complex as the one we perceive ourselves to be in. This raises a disconcerting thought: perhaps that is what our universe really is.

It is fascinating to speculate whether hyper-intelligent aliens already exist in some remote part of our cosmos. If so, would their brains "package" reality in a mathematical language that would be comprehensible to us or our descendants?

Martin Rees is professor of cosmology and astrophysics and master of Trinity College at the University of Cambridge. He was appointed Astronomer Royal in 1995 and is President of the Royal Society. This article is based on contributions to a discussion by a panel that included mathematicians Michael Atiyah and Alain Connes about the relationship between mathematics and science.
It's interesting to think about how the basic physical laws of our universe might be what we would use as a starting point in learning to communicate with an alien species from far, far away. In The Biocentric Universe and The Biocentric Universe Part 2, we've talked about the amazing new theories using "retro-causality": it has now been proven that observations made "now" can affect certain indeterminate conditions back "then". If this is the case, is it possible that the amazing amount of bio-diversity that we see around our planet might also be giving us more glimpses into what alien life is going to look like than we realize? In my book and this blog, I've talked about how there could be other completely different ways of expressing matter and energy that would still rightly be called "life", but perhaps those other formulations exist only within other parts of the multiverse landscape. Perhaps when we do finally find life elsewhere in the universe, the "fine-tuning" of our universe's conditions will have created forms that only seem as alien as the strange assortment of creatures we can find on our own planet. And if biocentricism is true, then it might be that the alien race we eventually encounter could have come from a first spark of life that appeared billions of years before life started on earth, and that it was actually that alien life-form that performed this reverse-fine-tuning of our universe's basic physical constants to allow all life as we know it appear within our universe!

Enjoy the journey,

Rob Bryanton

Next: Top Ten Tenth Dimension Blogs, July 09 Report

Mariana Soffer said...

I love the idea of infinity, and also thinking about it. Here is how this writter thinks about language and infinity, instead than about numbers, which I find very interesting and mind challenging,

Korean Culture: How do you see yourself as a writer? Do you have a message? Are you an ideological writer? An art-for-art’s-sake writer? An experimental writer? All of these?

Ch’oe: I guess critics like to make these distinctions, but it seems to me the true nature of creative writing is to be found outside such classification. To be sure, I have all of those tendencies you mention. A variety of them exist in all writers. If we really want to depict the infinite scope of reality, then we need to mobilize all of those tendencies. It’s precisely that infinity, shown to us by people and reality, that makes us write. The simplest fact that defines a writer as a writer is the expression of this infinity solely through language.

Mariana Soffer said...

By the way I did not comment you before cause I was struggling between 2 post to post. But have you seen what I posted this exact same day? inifity is called, another coincidence I guess.
take care my friend

Anonymous said...

Hi Rob,

Just had a question, about alien mathematics. As you may know, our mathematics is base 10. I was thinking what if there mathematics was base 7 or something like that. Infinity wouldn't differ in a base 7 set of mathematics but I just wanted to see what you think about that. :)

Anonymous said...

Hi Rob,

Just had a question, about alien mathematics. As you may know, our mathematics is base 10. I was thinking what if there mathematics was base 7 or something like that. Infinity wouldn't differ in a base 7 set of mathematics but I just wanted to see what you think about that. :)