Mathematics and Free Will

[shane.mcneil]

I'm reading a book about the mathematics of the physical world and how mathematics seems to be the language of the universe. Thus the natural world is predicatable, once we understand the math.

I'm wondering how far we can apply that. Does it apply to everyday life and the decisions we make? Do we have free will or are our actions mathematically predictable?

In asking this I mean are there scientific answers not just philosophical ones.

Regards, Shane.

[mjc (Mark)]

Its a very good question.

However, if mathematics was the language of the universe - and if we knew the mathematics completely - and measure the universe precisely - then we have pre-determinism - which is related to the thread title.

I don't think we can either know the mathematics well enough or measure physical phenomenon with sufficient precision to conclude that we have a deterministic universe - and deterministic actions of indivdiuals (compare with free will from thread title).

Even if it were theoretically true (should such a conclusion ever be reached) you'd need a computational machine at least the size of the universe to model the universe in real time - and that isn't practical. A small computer can simulate a mainframe - but not in real time.

Then there's Godel's Incompleteness Theorem - for any formal language language of sufficient complexity - it will either be incomplete or inconsistent - I'm not sure the universe reflects that.

Then there's quantum mechanics - where we can't know the precise nature of events on small scales (maybe thats the answer to my first query).

I believe that mathematics is a great modelling tool - but it isn't the real thing. However, I believe that mathematics exists as something independent from the physical universe (I know that sounds weird - but an implication is an implication and they are "discovered" not "defined").

Further, I Believe that the existance of mathematical truths are of great philosophical imortance. Cohen and Nagel "An Introduction to logic" - original publication 1934 had a great swing on logic - and if I recall correctly an implication exists regardless of whether man [or machine] thinks about it but an inference is temporal and requires a "psychology" [some processing must be done].

Bullet point: maths exists - universe exists - but they could be two dfferent (though closely allied) worlds.


Mark

[avandonk]

The only computer capable of predicting the future definitively is the Universe itself at about one second per second.

Even the so called quantum computers are merely very small subsets of the Universe.

In my humble opinion there is no such thing as eternal predermination. Sure we can predict short term. Even the orbits of the Planets are chaotic and unpredictable long term.

The idea of a clockwork Universe died with Quantum Theory and Chaos Theory. Godel did his bit as well.

Why chaos theory does not apply at the quantum level is that it is quite difficult to have feedback from indeterminate states.

Bert

[avandonk]

The take home message folks is that your fate is not predetermined. There are a lot of things you cannot control such as the choice of parents. It is up to you and you alone what you do with your life on the bits that you can control. It is nobodies fault but yours if you screw up.

I have to live with my mistakes as much as when I get it correct.

So should we all.

Bert

[bojan]

Originally Posted by avandonk

The take home message folks is that your fate is not predetermined. There are a lot of things you cannot control such as the choice of parents. It is up to you and you alone what you do with your life on the bits that you can control. It is nobodies fault but yours if you screw up.

I have to live with my mistakes as much as when I get it correct.

So should we all.

Bert

Very much so..

[Robh (Rob)]

Shane,

Very interesting discussion.
What does predictable mean?
Weather forecasters try to predict the weather for tomorrow and as far as a week way. Using recorded weather data, analysis of the data will give the most likely prediction for the weather. More and more data can be factored in as our supercomputers get more powerful. The implication is that certain factors A will result in event B. However, it would be a foolish forecaster who says with 100% certainty, it will be sunny at midday tomorrow!
Consider this experiment. I throw a die 1000 times and get roughly the same number of 1s, 2s, ... 6s, around about 167 in fact. However, in practice, I don't expect to get exactly the same frequency of each (in any case, 6 does not divide 1000 evenly). The mathematics can model the expected results but I cannot say that if I throw the die six times, one of those throws will be a 6.
Now, let's say I set my task to design a mechanical arm that throws a 6 every time. The die is placed in a rigid seat on the arm in exactly the same orientation each time. I spend 100 hours balancing the arm and adjusting the tension so that it throws the die exactly the same way. Initially, I just can't get it to land a 6. Eventually, adjustments give me some success and it throws some consecutive 6s but goes random again.

So what's my point? To make a certain prediction, I need exactly the same initial conditions acted upon in exactly the same way. In the case of weather, data is based on past weather conditions. At no time in the future will those conditions be exactly the same as in the past, so I cannot make a certain prediction. In the case of the mechanical arm, I can never control all factors that allow the arm to throw in exactly the same way every time. In any case, each throw of the arm will create the smallest wear on it so that the next throw will have different initial parameters.
The strength of mathematics is in modelling an expected outcome. We may be able to model the formation and structure of the whole Universe, its galaxies and filaments, but we cannot reproduce the exact Universe we live in.
Hence, the formulation of the Butterfly Effect which describes sensitive dependence on initial conditions in Chaos Theory. Small differences in initial conditions can result in large variations in behaviour and produce a markedly different end result.

I'm not going to debate whether our free will is an illusion or not. if it seems we can make a conscious choice, yes or no, left or right, that's free will. How much our physical makeup (genetics) and our experiences influence our choices is a debatable point. However, at any particular time, the choices you make will depend on a different set of conditions; the decision you make today may be different to the decision you make tomorrow. No two people have exactly the same personalities nor the same experiences, so we react differently to similar circumstances. From past experience, you may be able to guess what your actions might be under certain circumstances but you cannot say with certainty what your decisions will be.

Regards, Rob.

[shane.mcneil]

Thanks for your comments everyone. Food for thought.

I was thinking along the lines of calculating thoughts. We can calculate where a planet will be because we understand the math. We can calculate what atoms will (probably) do for the same reason. So when all of the atoms vibrating away in my brain produce a thought, is that able to be calculated? Is there a mathematical expression that describes it? If not, how does mathematically predicable patterns in nature become unpredictable in our brains? I guess I am asking what is consciousness????

I believe we have true free will, but I am wondering what the scientific explanation is for how it exists in a mechanical/mathematical universe, if that makes sense? I know there is a lot of philosophy on this subject but I'm more interested in science than philosophy.

Thanks again, Shane

[bojan]

Originally Posted by shane.mcneil

I know there is a lot of philosophy on this subject but I'm more interested in science than philosophy.

Thanks again, Shane

Have a look here:
http://stanford.library.usyd.edu.au/...qm-copenhagen/

[shane.mcneil]

Thanks Bojan. I slugged my way through it. Can't say that I understood it all. I guess you are saying that Quantum Physics may hold the answers to such questions.

Many thanks again, Shane.

[Nesti (Mark)]

Shane, I've been struggling with something similar for some time. I have been trying to understand how is it possible for Free-Will (Freedom of Choice) and deterministic properties of the universe to coexist peacefully.

The funny thing is-is that it seems to be entwined with time and, well, just about everything else actually.

A while ago, I stumbled upon two papers from Aharonov. They describe quite a bit about what where you're going.

I won't bother explaining anything, I'll just give you the links and let you read it for yourself.

If you read the Summaries first you'll get a good mental picture before reading the bulk.

For both doc's, just click one of the download options in the top right of the web page.

New Insights on Time-Symmetry in Quantum Mechanics
Yakir Aharonov and Jeff Tollaksen
http://arxiv.org/abs/0706.1232

Two-time interpretation of quantum mechanics
Yakir Aharonov and Eyal Y. Gruss
http://arxiv.org/abs/quant-ph/0507269

Hope you enjoy them.

Cheers
Mark

PS, Aharonov was a student of Bohm and I think it shows in his literary style.

[Robh (Rob)]

Hi Shane,

I thought I'd come in on this one again but tackle the probability elements from a new direction.

In quantum mechanics, Heisenberg's uncertainty principle basically states that, at any particular time, you can't simultaneously measure to arbitrary precision all the properties of a particle (e.g. position and momentum). The greater the precision of one measurement (e.g. position), the less precise the other (e.g. momentum). Values become a matter of probability.
The significance of quantum theory is that it's description of nature is essentially probabilistic.

In classical mechanics, if we know the exact state of a system at any time, we can theoretically calculate its state at any other time. A classical description is deterministic. The difficulty to date has been reconciling the deterministic theory of general relativity with the probabilistic theory of quantum mechanics. To unify quantum mechanics with gravity some deterministic flavour may have to be used.

However, whether nature is deterministic or not, the underlying processes are usually so complex and chaotic that we have to resort to stochastic methods anyway. In practice, reduction of initial conditions, including approximation of measurements, can result in large deviations from expected behaviour over time (sensitive dependence in chaos theory). Example, it is impossible to predict Saturn's orbit in 100 million years with any accuracy. Unexpected influences over time can also cause havoc with predictions e.g. a large unknown body swoops past Saturn in 1000 years time.

The Universe today reflects the chaotic nature of the way energetic particles and matter were distributed after the Big Bang. It appears galaxies lie in a scaffold of randomly distributed filaments across the Universe. Any model of the origins of the Universe can at most build a similar universe from probabilistic considerations but not one that is exactly the same as ours.

In my mind, a world of mathematical approximations and probabilities fits in quite well with the notion of "unpredictable" thought. Our actions are not mathematically predictable because all the interrelating factors that influence our decisions are far too complex and not repeatable. For this reason, we have free will. For each new set of events, we make an approximated assessment and a probable forecast and then decide on a course of action.

Regards, Rob

[avandonk]

Has it ever occurred to any of you that your brain is fundamentally functioning at the quantum level. The fact that it is very fuzzy compared to modern solid state computers does it not make you curious.

When a solid state machine can see the beauty of it's Universe it will have attained self awareness.

Most of these arguements are circular by definition. When a computer has the urge to have a leak in the middle of the night I will sit up and take notice!

Penrose is starting to think along the same lines.

Mathematics is just the software. The miriad of quantum states of the hardware is the scary bit.

Would you believe C60 or Buckyballs diffract through two slits. This means that one Buckyball went through both slits and interfered with itself!

We are all just wave functions that only exist when we get online or are squeezed through two slits!

Bert

[shane.mcneil]

Thanks Mark for those articles. I will get into them. Though I may need you to summarise the summary for me as I don't really know too much about this.


Thank you too Rob. I was wondering about calculating probabilties. (Pardon me if I sound ignorant here) I understand that it is difficult to determin outcomes as there is always something we don't know. And that small amount of unknown can lead to a rather large unexpected outcome in the end. But if we theoretically did know litereally everything, could we determin an outcome or is there something fundamental about the universe that stops that from happening? I always imagined that any short fall in our predictions was because of a lack in our knowledge. That randomness is an illusion. We see something as random only because there are factors we didn't take into account.

When I apply that to thoughts and consciuosness it seams to me that either are thoughts are the result of theortically determinable processes (not that we ever could hope to acheive that level of determination as you said) or I am just plain wrong in my original thought (again).

It's fun thinking about it anyway.

Best regards, Shane

[Nesti (Mark)]

Originally Posted by avandonk

Penrose is starting to think along the same lines.

Sir Roger coped a lot of flack for that...his Microtubes idea, although wonderfully logical, is in tatters.

Bell destroyed about a thousand ideas in one blow, quantum fluctuations in Calcium ion Microtubes was one of them.

You often talk about waves, have you read Karl Pribram's ideas?
"The senses themselves were ‘lenses’ for observing the information as it was being unfolded. It was also suggested that memories were, by association, connected to thought, and that neural activity unites the two to form a conscious experience and consciousness."
Karl's ideas ties-in with Bohmian Mechanics (and Implicate Order), where a universal standing wave holds information, and at any time and place in the universe, information may be unfolded into spacetime.

In the case of your Buckyballs, they are merely information which enfolds and later unfolds between the slits...and everything comes back to wave-like properties because of Bohm's universal standing wave.

[shane.mcneil]

Has it ever occurred to any of you that your brain is fundamentally functioning at the quantum level. The fact that it is very fuzzy compared to modern solid state computers does it not make you curious.

Hi Avandonk

I can't even pretend to understand Quantum Physics so stop me at any time. I thought Quatum effects only mattered on a quantum level. Once you get to the macro level they no longer have a significant impact and that is why the universe is predictable. If so I would have thought our brain is a macro system and thus predictable in some way.

[Nesti (Mark)]

The macroscopic world is more of 'an illusion of sheer numbers', whereas the quantum landscape paints a truer picture of reality (albeit counter-intuitive). Our large scale reality is [mostly] derived from quantum events, not vice-versa.

An example of how quantum events cascade into a smooth stable reality.

Consider this analogy: a casino. If we observe an individual player winning and losing over a period of time, we see a win here and a loss there, a seemingly random series of events. However, if we observe the player over a great length of time and tally up the results, we notice a trend appearing, a tendency emerging out of randomness. Since casinos have the odds slightly stacked in their favor, our player is progressively losing money to the casino, especially if the betting amount and regularity is fixed; just like quanta. This is basic game theory in action, whereby the chance of the casino winning slightly outweighs the chance of the gambler winning. The odds are literally stacked in the casino’s favor.
What do you think happens if millions of players make hundreds of individual bets of an average amount over a long time? Remember, at the core of existence, the ‘period of time’ (time) is actually irrelevant and only ‘individual bets’ (event numbers) and ‘average amounts’ (quanta) mean anything. Mathematics allows us to calculate, very precisely in some cases, exactly what the casino stands to win over a given period of time. Also, accuracy increases if the number of individual bets increases. So from the casino’s standpoint, a million punters betting $1 at a time, over 100 bets, presents a much more stable prediction than 100 punters betting $1 million in just one bet. Incidentally, this is precisely how manufacturing companies determine rates of flaws/failures in mass produced goods. If we apply this mathematical process to trillions of trillions of particles, which in turn are involved in trillions of trillions of individual events, we see the trend emerge. This trend is the smooth progressive uniform change in matter from one set of states and values to another, then another and so on. This is cause and effect, causality, this is also time itself.

Notice two things; that Free Will is still missing in this analogy and also the we need a cause of the odds to be stacked off-balance in the real [quantum] world for time to emerge...if time emerges through the numbers game in the first place.

[shane.mcneil]

Thanks for explaining that Mark. So would that mean that if out thinking occurs on a quantum level, then trends in our thinking would be revealed just as it becomes obvious that the casino is winning?

[bojan]

Originally Posted by avandonk

Has it ever occurred to any of you that your brain is fundamentally functioning at the quantum level. The fact that it is very fuzzy compared to modern solid state computers does it not make you curious.

Very often thoughts like this one made me think about what consciousness is all about (and why me is ME and not someone else..).
Is it just the number of calculations per second or something else? Perhaps the answer is in fuzziness? But how?
Is AI (and artificial consciousness) just a myth.. or is it plausible?

[Paddy (Patrick)]

all I know is that when I have my free will, I avoid mathematics...

[Robh (Rob)]

Originally Posted by shane.mcneil

Thanks for explaining that Mark. So would that mean that if out thinking occurs on a quantum level, then trends in our thinking would be revealed just as it becomes obvious that the casino is winning?

Shane,

In making a prediction, one really needs to differentiate between a specific outcome and an expected outcome or overall trend.

Consider the following ...
A poll of 100000 voters, predict that the Liberal Party will win the next election by a huge margin. The voters in a particular electorate reinstate a Labor Candidate.

In a casino, the game odds are weighted in the house's favour. Generally, the more the games played, the greater the casino's profits. On a one-off night at the casino, a guest bets $100 and wins $10000.
A specific outcome can go against an overall trend.

Photons produced by fusion in the core of the Sun travel a few millimetres before being absorbed and then re-emitted in a random direction. Using a random walk, we can calculate the average "photon travel time" from core to surface. It works out at around 100000 years. The range is anywhere from 10000 to 170000 years. However, it is impossible to pinpoint the actually photon path nor its position at any time t.

Now, consider a boat adrift at sea. In theory, the course of the boat can be plotted. The boat should be headed in a certain direction due to prevailing sea currents and wind patterns. However, in practice, approximation of initial conditions makes the course chaotic. A prediction of the position of the boat over time becomes increasingly less accurate.
The deterministic nature of any system does not make it predictable.

Trends in our thinking do not make our choices in a particular circumstance predictable.

Regards, Rob