Mathematicians who call themselves ultra -thinning think that extremely large numbers are delaying science – from logic to cosmology.
For some people, the infinite It is a substitute for a process, such as counting, which could last forever. For others, it means an incalculably large number. In either case, relate it to human experience becomes difficult.
Although the standard image of cosmology tells us that the universe is infinite, without limits, we also know that, in a way, it has a “limit” – a bubble within the cosmos we call observable universe, delimited by the light that has been traveling towards us since the big bang. Anything beyond this is unknown.
As the 1960s writes a “small but tireless” contingent of mathematicians, philosophers, computer and physical scientists have argued that perceiving finitude is important.
They are called ultrafinitistas and warn that the fact that you cannot be too trusting in numbers like 10100that escape our experience in the real world. About infinity? “This is just an illusion,” says Doron Zeilberger from Rutgers University, New Jersey, to New Scientist.
Historically, the ultrainitist movement has often been considered radical and incoherent, but its defenders say that huge numbers and infinity are undermine the foundations of science, from logic to cosmology.
In April, there was a conference on Ultrainitism at Columbia University, which brought together investigators “concerned about the role that Infinity plays in mathematics,” describes New Scientist.
Is it possible to abandon infinity?
If the ultinishist project can remove the infinity from our mathematical toolbox, we may then have to face the possibility of the universe, even beyond the limits of the observable universe, to be in fact finished.
How can the laws of physics allow this? During the conference, the physical Sean Carroll presented a physical model for an ultrainite universe.
Built in quantum mechanics, the universe model of the Johns Hopkins University scientist in Maryland (USA) remains spatially infinite, but has only one finite number of allowed quantum states.
The result is a universe that is periodic in time – It changes, but always ends up returning to your initial state.
This contrasts strongly with the widely accepted point of view that our universe had a starting point on Big Bang and, following the laws of physics, such as those of thermodynamics, it continues to expand.
However, Carroll showed that, carefully adjusting his model – for example, limiting the ways as entropy, or disorder, this universe can float – could avoid violating these laws. In doing so, it provided a basic basis for the functioning of a finite universe and the way the complexity of reality, such as the shape of spacetime, can emerge from this universe.
It is good to clarify that, in his presentation, Carroll did not argue that we live in this kind of finite universe, but also did not reject it totally, saying it was “Perfectly conceivable”.
With potential benefits in a series of scientific disciplines, will New Scientist question ultrainitism seriously as an alternative view of the foundations of mathematics, even if it is just to compare the standard approaches?
