August 12. 2008 03:31

Hi Jim

Interesting website. I'm not a subscriber to New Scientist; so I can't read the Penrose's article. But I think your missing where he's coming from. If I recall correctly, Penrose is a Platonist re. maths: he thinks that numbers are discrete entities that exist in a abstract realm and what mathematicians do is "discover" these objects and their possible relations. The opposing view is that mathematics is merely invented by humans. The problem with this latter view is: if it is a matter of invention how come we can't invent a fundamentally different system? The problem with Penrose's view - and this is where he's coming from re the quote in your blog - is: if mathematics is constituted of entities and relations independent of our existence, could we not be mistaken inidentifying these abstract entities and their relations? (Saul Kripke in his book "Wittgenstein on Rules and Private Language" discuss this issue at length and extends the discussion beyond maths to language and communication in general). I think both views are, on their own, wrong, but a combination of these two "opposing" views can be forged (though here is not the place for that lengthy discussion and it's been a few years since I looked at the issue). Anyway, in your discussion of 2+2=4 applied to the "2-mile straight line" example, you're superimposing an (abstract) mathematic relationship (in Penrose's view) onto a physical relationship but assuming the relationship between the two is of the same kind. Zeno uses this exploits this confusion to "prove" motion is impossible!

All the best

Nathan

nathan

August 13. 2008 01:19

Thanks for the response Jim. By-the-way, sorry for sloppy typing / grammar: I multitasking!

"Penrose references David Hume's assertion that induction is impossible: that no matter how ofter you calculate 2+2 and get 4, you can't be certain that you will get the same result the next time."

Hume's point is not that induction is impossible (as he admits we make inductive observations all the time and they are very necessary for everyday living!), rather we cannot logically deduce them from our experience. We cannot deduce all the properties of macro-objects from quantum laws, doesn't mean (necessarily) to say those objects don't exist! Penrose appears to confuse the analytic truth that 2+2=4 with the empirical process of calculation - i.e. the inductive observation: just because I got 4 in past when I carried out this operation I will get 4 in the future! That does not affect the truth that 2+2=4, because that truth does require anyone to observe it to be true! It is true independently of our existence and the existence of space-time & matter.

"if we live in a programmed reality, we are only living by, and believing in, the laws of math that have been imposed on our reality. Which may not be the true laws of mathematics in the deeper reality."

Let me put it another way: where is your true laws of mathematics located - how is "trapped" or "concealed" there? By what methodology? (If I get time I'd like to expand on this point later because I think your programmed reality idea is highly viable and hopefully when I read your book I will get a better idea of where you're coming from).

Actually, let me just say straight out that Penrose is wrong and what gives me the confidence to say that is not I'm in his mathematical league of genius (I'm pretty poor), rather it conflicts with his other arguments. This conflict is pretty deep, but let me illustrate it a crude form. Take Penrose's tiling Euclidean plane argument as used against certain artificial intelligence models; a person can look at the tiles and see that they can be fitted together in a repetitive fashion ad infinitum. A computer, say, would have to have that insight provided for it, otherwise it would continuing tiling forever! Here Penrose is drawing attention to the fact that we (persons) can, for want of a less obscure phrase, "intuit" certain truths; ones that cannot be merely "captured" or "codified" in a rule. Now think about this in relation to 2+2=4. What is 2+2? To answer that question did you apply a rule? Or did you remember the answer? Or is the case that whenever someone asks that question you always answer "4" because it's the socially acceptable think to do? May be you forgot how to perform addition and therefore had to consult a text book (but does the text book know - understand - the answer?). My point is Penrose has a confused notion as to the nature of following a rule - a rule doesn't tell how you ought to understand it, it application in which understanding arises and the ability to correct yourself and see possible conflicts with other rules and their application. Think about learning to count - the teacher give places 2 rows of 6 coins in front of you and sets the following 3 rules: (1) point to each coin and tell me the correspondingly cardinal number (1, 2, 3, etc.); (2) don't miss a coin and point to the same coin twice; (3) when I ask you "outcome" give me the numeber of the last coin counted. The teacher gets you to count the row separately and then together. All seems to be going well, except when the teacher asks you to count the 2 rows of coins together and she asks "outcome?", you say "13". Teacher is suddenly not happy! "But last time I asked you "outcome?" you said "12!" - you must have made a mistake!" Most likely you counted the same coin twice at some point and didn't notice this; you got distracted. Now it obvious to the teacher you made a mistake because you gave her two different values when asked for the outcome, however if you back at look at the rules, nowhere does it say - explicitly - that different outcomes are an indication of a fault in the application of the rules. This is where learning comes in and why mistakes are important.

Apologies to Penrose, I got carried away - I haven't read the full article and so I'm guessing why he made these statements.

Thanks for reply. Sorry mine's a rush.

Nathan

nathan

August 13. 2008 09:48

Hi Jim

Apologies for being belligerent on this this matter, but I would like to take issue with on your statement:

"I do realize the difference between applying math to the abstract and to physical relationships. But to make that distinction, you have to agree that math shouldn't be applied to physical systems. In which case, is it just philosophy?"

As an individual who spent ten years of his life in academic philosophy, I beg to differ on your last sentence; however, observing the output of my former colleagues, I can identify with that sentiment! I want to focus on your assertion that, "to make that distinction, you have to agree that math shouldn't be applied to physical systems." Why? Because I think you are assuming a certain kind of relationship between (mathematical) models and their direct simulation (or, in alternative parlance, "description") of reality. To make this point, I won't directly to refer examples from so-called "pure" maths but to the applied maths used in developing models of "reality" - e.g. physics is a "highly mathematised" subject.

There's a certain strand in the philosophy of science that, because of the success of the reductionist method of explanation - i.e. a given physical event / object can be fully understood / explained by examining its constituent "parts" and their interrelations - i.e. that we can reduce the macroscopic and microscopic world to some putative "theory of everything". While I think the reductionist strategy has been amazingly successful, that success has blinded its proponents into a carte blanche acceptance of its explanatory power. Take one example of this igiolgical position: water is H2O (I'm using "is" here to mean "identical to" in the spirit of "Leibniz law" (i.e. water and H20 share all the same properties and therefore can be consider as being the "same thing")). Examining the structure of water in terms of it's molecular make-up has been a tremendously successful model. However, is water really the same "thing" as H20? Before I answer my own question, let me introduce the metaphysical concepts of identity and change. Would you agree that in order to say something has changed, you have to be able to identify the object in question that has undergone change? Now water can change: it can exist in different "physical states" - gas, liquid and solid. Can a moecule of H2O exhibit these kind of state transition? Individually considered "no"; collectively, "yes". That implies the "collection" is greater than the sum of its parts - the whole cannot be explained (entirely) in terms of its parts. (Look up the definition of "compound" and "mixture" in any chemistry text book.) To compare water with H20 is an example of model approximation; it is useful in making predictive claims re the properties of water to think of it as a collection of H2O molecules.

In "reality" - in the macroscopic world, when do you come across a sample of water that is entirely made up of H20 molecules that have a fixed, individual, number of electrons "dancing" round the nucleus? A so-called "pure water"? And what about "heavy water"?

In short, I would say a (mathematised) model is useful, but it is not identical to reality. Becuase a model is not identical does imply it is not usefule; therefore I disagree:

"math shouldn't be applied to physical systems".

Best regards

Nathan

nathan

September 8. 2008 23:16

That lesson of 2 + 2 = 4, was in a slightly different manner, the impetus for my interest 40 years ago in the nature of reality. Sixteen years old at the time in high school physics, my teacher, Mr. John Scanlon, explained to our class that 1 + 1 only equaled 2 because we believed it to be so because each time we've added it up so far, that's the total that we arrived at. But there was no guarantee that it would add up that way the next time. It was as if the solid ground had dropped from under my feet, and I was floating in the middle of nothingness. Nothing was true. It became a starting point for a life of a universal quest for understanding, which, I'm happy to say, I have achieved.

Michael Galileo

September 20. 2008 07:18

Jim,
I'm not so certain about Mr. Scanlon's level of insight as he swore, incorrectly, that I would never pass his class, lol. But he did pique my interest with that statement.

Regarding some of the other comments that have been posted here, I'd like to say that I see the mathematic formulas developed by man as extrapolations of potential elemental behavioral patterns under different conditions. As such, they do not dictate, but can define the probabilities of outcome from the interaction of different elements, sometimes digits, in varying environments. When math is seen this way, it has application across all aspects of this perceivable universe, including physical systems and relationships.

The ultimate math formula which rules all outcome and manifestation in this universe and the one, from which all others are merely derivitives is of course, Un=Un-1+Un-2, or the Fibinocci Recurrance of Whole Numbers; The Golden Ratio, or Golden Mean. I have even found a way to apply this formula to all of mankinds subjective world to expose the underlying "Lowest Common Denominator" that rules all outcome of both man and nature. Let me explain.

Realizing that man exists and experiences this universe from the 10 to the zero power perspective, one must convert the electromagnetic power that causes the ionization and polarization that drives the evolution of all things in this universe to a proportion relative to mans perspective. One must first quantify the "now" in order to mathematically formulate values of the "before now" or "subsequent now". To that end, one would have to agree that the main system of measurement most used by man to evaluate time and distance is a year. We measure the size of the universe, our life expectancy, our length of relationships, carreers and prison sentences on Earth years. An Earth year as we know is the amount of time that it takes for the earth to orbit the sun. That distance is approx. 564 million miles. we travel about 1.6 million miles a day, and it all breaks down to 18.5 miles per second, which means that a second is approx. 18.5 miles long (yes, they can vary a bit, but not much).

A year is made up of seconds. If one lives to be 72 years of age, that is approx. 2.25 billion seconds, but the universe only gives them to you one at a time, and just as each whole number in the Fibinocci series is a total of the two whole numbers before and contains all of the accumulating value since the first number (0,1,1,2,3,5,8,13,21,34....) each second that we experience is a total of the choices made in each prior second since our first, and ultimately since the first moment of this universe 15 billion "years" ago. Just like with the Fibonacci series, if the choices are "good" ones our evolution continues to grow and prosper, but if the value of the choices are less than their potential allows, then the ultimate experience is less than it could be, and all by choice.

A second is to the building of mans subjective reality as an atom is to the construction of matter. Any piece of matter is only the way that it is because every atom that composes that matter is as it is. If even one atom were different, it would be different, albeit, depending upon the mass of the matter in question perhaps imperceivable. If more of the atoms were different, the resulting matter would be different, just like the second by second choices made within mans subjective reality which causes it to be as it is in any moment or second. "As Ye sow, so shall ye reap" is the biblical take on it, and it's the basis for the concept of Karma, all of our actions and choices that continually come to manifestation in our reality.

Hope that's not too convaluted to follow. I think it shows the practical application of at least one math formula to all aspects of this universe, and dependable too, since it's the formula by which we can trace time moment by moment back to the beginning of the universe without fail, and the one nature uses to build it's world as well.

Michael

Michael Galileo

December 21. 2008 10:05

Roger Penrose Agrees with Me

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December 30. 2008 22:16

I agree 2+2 may not = 4!

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January 6. 2009 14:48

2+2 may not = 4! ?

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January 9. 2009 22:01

As life science person (specifically animal science) I can assure you that 2 puddles plus 2 puddles equals 1 puddle. I prove this every time it rains. Draining the numerous wet spots in pastures involves carving minute waterways with my boots to combine puddles, then using a shovel to create a drainage ditch that allows all water to flow downhill to (wherever puddles go ... usually/hopefully to the creek). One puddle from many.

That aside, as a child I took the liberty of using the inside the front cover of my mother's circa 1903 version of The Wizard of Oz to prove that 8 plus 8 equals 88. There was no question in my mind that I was correct, and no one challenged me. Now I realize that no one argued my point because I was so insistent that I was, indeed, correct; and well, "why bother? This kid doesn't understand math anyway."

I think the fact that I chose that particular book among many others is some sort of odd, serendipitous proof that I had it right. In a Wizard of Ozesque world, I'm still learning and questioning (isn't that the point?) In working on a NF narrative about Lee the Horselogger, who who started with $75 and has managed to travel across the United States from Montana and back with a homemade wagon pulled by his horse logging team, I've learned to 'question the man' and look beyond the curtain. Lee often uses allegories to help people understand life with examples such as the (roughly translated) Buddhist teaching “All instruction is but a finger pointing at the moon, and those whose gaze is fixed upon the pointer will never see beyond.”

Thanks to Karen for pointing me to you, Jim!

Sally HH '71

sally

January 21. 2009 12:31

sometimes when I have drunk too much coffee I think 2+2=5 is that correct?

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February 7. 2009 10:35

This post makes my head hurt and reminds me of studying critical theory at Uni.

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April 1. 2009 01:14

I thought the answer was 42.... but I blinked.....

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June 28. 2009 22:27

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July 14. 2009 23:31

What is the basic difference between philosophy and religion?

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July 18. 2009 09:55

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July 19. 2009 22:52

Which do you believe in this philosophy "Essence before existing" or "Existing before essence."

Jlmark Santos

August 8. 2009 20:21

This reminded me of another book that I liked for much the same reason: Inward Bound by Abraham Pais (1986). It's basically a history of modern physics, but unlike most such books does not shy away from the mathematics (without which the physics would make little sense). In fact, I just pulled it off of my shelf and see that one of the testimonials on the back is from none other than Roger Penrose...

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September 19. 2009 15:59

"how do we know that we aren’t in a dream right now???" - Just like the concepts in the Matrix. Is this reality or just what we think is reality. We will never know unless there is a glitch and we see the alternative world - but if we do who would ever believe us?

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October 20. 2009 03:34

this remind me on my class on philosophy. this is just logic where everything comes from a pure reasoning.

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October 24. 2009 19:47

Very interesting read thanks.

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October 25. 2009 23:37

This subject is really makes my headache. I don't care if i am just dreaming or I am not in really world right now. All I care is I know I exist in this particular place and time.

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October 26. 2009 21:48

Great post.

waggi

December 10. 2009 07:27

you have to agree that math shouldn't be applied to physical systems. In which case, is it just philosophy?

My point is actually a little different, although perhaps not that clear. It is that if we live in a programmed reality, we are only living by

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