In the very least, we asume the universe can be described by only math.
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Yeah⌠i agree with youâŚ
For some definition of mathematics. My view is that computation is best viewed as something distinct from maths. Maths can describe the current state of the universe (within the limits of quantum uncertainty), but computation describes the transition from one state to the next. There are no shortcuts: to find out what the future holds you have to run the program.
And what is true of the universe is true of the brain.
Maths was not able to define what is uncertainty even computation canât do that⌠Computation will show the picture but it will never tell how,why,what of the picture⌠i believe if we define what is a uncertainty, then maths will be usefulâŚ
Science is not an assumption. Science is a process for developing models that approximate the behavior of reality. The scientific method is the original data science: collect data, generate a family of models (hypotheses), evaluate/tweak the models to better replicate the observed data, rinse/repeat. (Oh, and donât forget to publish your results). Each model makes use of simplifying assumptions that make the problem computationally tractable. Whatâs remarkable is that these assumptions are often valid to the extent that they enable these models to predict the behavior of physical systems with amazing accuracy.
This is actually an observation. The fact that this behavior is observed in nearly all material objects provides evidence in support of the conclusion that the theory of gravity is a practical model for this particular aspect of reality.
See also the Uncertainty Principle, probability theory, and stochastic processes. Some people think that uncertainty means that something is unknowable. Thatâs not quite true. Itâs more like something is knowable within some prescribed bounds of accuracy. This accuracy bound may be the result of the limits of measurement or due to invalid or incomplete assumptions in a model.
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The universe is what it is. It is most likely not made up of math. The choice to use mathematics as the symbolic system in which to develop models of the behavior of the universe is a practical one. For physical phenomena, itâs simply the best system we have at the moment for this purpose.
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I donât know what it is that you are describing as computation, but I think if you actually look at the history of computation and information theory, youâll find a whole lot of math. (see Claude Shannon, John von Neumann, et.al.)
See also Finite-State Machine, which can also be expressed as a mathematical model.
See also Stephen Wolframâs computational irreducibility.
This would be a reasonable assumption if, in fact, every bit of information in the state variables is required to describe the system (i.e. no approximation or compression is possible). I would point out, however, that such a system would likely be incredibly brittle. For example, if any of those bits are flipped, it could conceivably create a system that would ultimately diverge from the unaltered system. The more robust a system is to minor perturbations, the more likely that there is redundant information available in the system that enables error-correcting behavior. The presence of redundant information permits data compression, the ability to error-correct suggests the possibility that this process could be mathematically modeled.
Evidence would suggest that the brain is a very robust system due to the fact that it is composed of neurons and synapses that are very noisy in their operation (subject to the physical and chemical behaviors of ions and neurotransmitters) and is being provided with input from sensory organs that are also incredibly noisy. This suggests to me that the processes of the brain can be modeled, and that model will eventually be fully described using mathematics.
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Hear Hear! Everything we know about the real physical world we know through science, with the help of maths. There is nothing else, and it works.
The maths of uncertainty is known in excruciating detail. QM and all that.
But I canât resist asking: ânearly all physical objectsâ?
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I would be remiss in my duty as a scientist if I didnât qualify my statements with the conditions that; a) I have not personally made all of these observations, b) there may be states of matter that we have not yet properly observed that do not behave according the the currently accepted theories of gravity (i.e. special and general relativity). For example: the terms âdark energyâ and âdark matterâ are currently used as place-holders for theories which may be able to explain some observed deviations from what our current models would predict about the motions of galaxies with respect to one-another (dark energy) and the distribution of orbital velocities of stars within galaxies (dark matter). Despite the remarkable success of the theories of relativity in just about every conceivable test that weâve thrown at them, there are still some discrepancies between our models of distant galaxies based on these theories and the actual observed data.
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