As the Pencil Fell

[Clifford Greenblatt]

In the natural scenario I have provided, the values of the constants of nature in question are not the only ones that can occur. A huge range of values are in fact possible, as are all the possible laws that can result from symmetry breaking. The constants and forces that we have were selected by accident–as the pencil fell–when the expanding universe cooled and the structure we see at the fundamental level froze out. Just as the force laws did not exist before symmetry breaking, so, too, did the constants not exist. They came along with the forces, all by chance. (Stenger 2000)


Materialism rejects the idea of the omnipresent Biblical God. Dr. Stenger's falling pencil illustration would, on the surface, seem to deny any form of omnipresence. However, a closer examination reveals an infinite omnipresence that is readily apparent to materialists. This omnipresence is in the form of mathematical relationships and values that are invariant to the way the pencil falls. For example, the value of pi is 3.14159265358979323 . . . no matter how the pencil falls. The infinite sequence of digits in pi would appear to be quite random, the product of pure chance, but every one of those infinite digits are absolutely identical in every part of every universe that could possibly exist. One may argue that the use of base ten in the representation of pi is arbitrary, but this makes the omnipresence even greater. We could represent pi in base 2, 3, 4, or any other integer. For any given radix, the value of pi is represented by an infinite, nonperiodic, sequence of digits. Every digit in the infinite sequence is perfectly invariant to the falling of the pencil in any place in any possible universe.

An uncountable infinity of values having the following properties are omnipresent throughout all of reality, invariant to the falling of the pencil. In any radix, each of these values is represented by a sequence of digits which is both nonperiodic and infinite in length. However, every one of these values are derived from a finite number of digits. An example of one of these values is the square root of 3. This value is derived strictly from the numbers 2 and 3, which are represented by a finite number of digits. There are an infinite number of radix possibilities by which the square root of 3 may be represented. The radix is always an integer, making it a third number which is represented by a finite number of digits. For any given radix, the square root of 3 is represented by an infinite, nonperiodic sequence of digits which is perfectly omnipresent in all of reality, being invariant to the falling of the pencil in any place in any universe.

[Jobar]

Welcome to the forum, Clifford.

For example, the value of pi is 3.14159265358979323 . . . no matter how the pencil falls. The infinite sequence of digits in pi would appear to be quite random, the product of pure chance, but every one of those infinite digits are absolutely identical in every part of every universe that could possibly exist.

...And you know this, how?

I'm not the physicist Dr. Stenger is, but isn't the value of pi dependent on the curvature of spacetime? Why must that curvature be the same in all possible universes?

I don't think we can say that any presence- that is, any concretely real thing- is infinite. Infinity is, as far as I can tell, a purely abstract concept, like imaginary numbers.

[john_v_h]

So, irrational numbers exist and they are, arguably, omnipresent. How do you leap from this premise to the existence of an omnipresent god? Is god an irrational number?

[Clifford Greenblatt]

Originally quoted by Jobar
...And you know this, how?

I'm not the physicist Dr. Stenger is, but isn't the value of pi dependent on the curvature of spacetime? Why must that curvature be the same in all possible universes?

The value of pi can easily be calculated by a digital computer using a reasonably simple algorithm. The curvature of spacetime does not enter into the algorithm at all. It may take forever for a computer to calculate pi to infinite digits, but the longer the computer runs, the more digits you get. Space has more curvature at sea level than on the top of Mount Everest. A computer on board the QEII and a computer on the top of Mount Everest, left to compute pi to ten trillion decimal places, will produce identical answers in all digits.


Originally quoted by john_v_h
So, irrational numbers exist and they are, arguably, omnipresent. How do you leap from this premise to the existence of an omnipresent god? Is god an irrational number?

It is not simply irrational numbers that are omnipresent, but derived sequences that are absolutely invariant. For example, if the square root of three was irrational in two places or universes but had a varying value, then the idea of omnipresence would be violated. This does not prove the Biblical God but it does present a strong case for the attributes of omnipresence and immutability being very much consistent with mathematics and science.

[Bookwyrm]

Originally posted by Jobar

I'm not the physicist Dr. Stenger is, but isn't the value of pi dependent on the curvature of spacetime? Why must that curvature be the same in all possible universes?


The ratio between the circumference of a 'circle' and its diameter in non-Euclidean geometries is variable depending upon the exact shape of the space under consideration, and the size of the circle; the value of Pi is nevertheless independent of the curvature of space-time, but only because it has been defined as the ratio between the circumference and the diameter of a Euclidean circle.

[Howard]

You don’t think there’s a pretty big stretch from an interesting mathematical concept to a sentient, all powerful being? This kind of gigantic inferential leap reminds me of New Agers latching onto Quantum Mechanical phenomena and using them to justify whatever brand of mysticism they are trying to sell - trance channeling, crystal healing, astrology, etc.. “See,” they say, “If that’s true then this could be true, too.” Could be, yes, but it’s little more than imaginative speculation.

[HRG]

Originally posted by Clifford Greenblatt

Neither pi nor the square root of 2, 3 etc. are part of our universe. They are part of the mathematical models which we use to (approximately) describe the universe. Big difference, IMHO ....

Regards,
HRG.

[HRG]

Originally posted by Bookwyrm
The ratio between the circumference of a 'circle' and its diameter in non-Euclidean geometries is variable depending upon the exact shape of the space under consideration, and the size of the circle; the value of Pi is nevertheless independent of the curvature of space-time, but only because it has been defined as the ratio between the circumference and the diameter of a Euclidean circle.

True.

Actually, Bourbaki's Elements de Mathematique define pi as the first non-trivial zero of the solution of the differential equation:

y'' + y = 0, with initial conditions y(0)=0, y'(0)=1

which doesn't talk about circles, radii, Euclidean geometry etc. at all.

(This is equivalent to the circle definition, since the solution is y=sin(x), and sin(pi)=0 .....)

Regards,
HRG.

[Jobar]

the value of Pi is nevertheless independent of the curvature of space-time, but only because it has been defined as the ratio between the circumference and the diameter of a Euclidean circle.

Ah. I recall reading an article in Scientific American about the effect of gravity on circles; one drawn about a singularity at the event horizon may be thought of as a straight line, as a light ray travelling along it will 'orbit' infinitely. So I knew that a non-Euclidian space (one distorted by, in this case, gravity) would not produce the same value for pi.

So, am I correct in saying that Clifford's argument reduces to "2+2=4 everywhere, therefore god exists"?

[Singularity]

Originally posted by Jobar
So, am I correct in saying that Clifford's argument reduces to "2+2=4 everywhere, therefore god exists"?

Unfortunately for Clifford, that does appear to be his "argument."

[rainbow walking]

Originally posted by Clifford Greenblatt
Materialism rejects the idea of the omnipresent Biblical God. Dr. Stenger's falling pencil illustration would, on the surface, seem to deny any form of omnipresence. However, a closer examination reveals an infinite omnipresence that is readily apparent to materialists. This omnipresence is in the form of mathematical relationships and values that are invariant to the way the pencil falls. For example, the value of pi is 3.14159265358979323 . . . no matter how the pencil falls. The infinite sequence of digits in pi would appear to be quite random, the product of pure chance, but every one of those infinite digits are absolutely identical in every part of every universe that could possibly exist. One may argue that the use of base ten in the representation of pi is arbitrary, but this makes the omnipresence even greater. We could represent pi in base 2, 3, 4, or any other integer. For any given radix, the value of pi is represented by an infinite, nonperiodic, sequence of digits. Every digit in the infinite sequence is perfectly invariant to the falling of the pencil in any place in any possible universe.

An uncountable infinity of values having the following properties are omnipresent throughout all of reality, invariant to the falling of the pencil. In any radix, each of these values is represented by a sequence of digits which is both nonperiodic and infinite in length. However, every one of these values are derived from a finite number of digits. An example of one of these values is the square root of 3. This value is derived strictly from the numbers 2 and 3, which are represented by a finite number of digits. There are an infinite number of radix possibilities by which the square root of 3 may be represented. The radix is always an integer, making it a third number which is represented by a finite number of digits. For any given radix, the square root of 3 is represented by an infinite, nonperiodic sequence of digits which is perfectly omnipresent in all of reality, being invariant to the falling of the pencil in any place in any universe.

rw: Seeing as a perfect circle is impossible in this universe, we can therefore conclude that a perfect god is equally as impossible...yes? That is also a conclusion that follows from your example. And are we to also conclude that, since pi cannot be ascertained conclusively, that an omniscient god would be equally unable to do so? Or is it the case that some portion of his sentience is infinitely engaged in following these random digits into infinity seeking a resolution?

[Oxymoron]

ARGUMENT FROM MATHEMATICAL NAIVETE

(1) exp(i*pi)=-1
(2) therefore , God exists.

The OP at best demonstrates (doesn't prove) an allegedly necessary - not sufficient - condition for an omnipresent creator. Some work to do yet, Clifford.

[Jack the Bodiless]

When physicists refer to a range of possible values for the "natural constants", they're referring to such things as the speed of light, the strength of the various fundamental forces, the mass of elementary particles, and so forth.

[Ellis14]

I see no need to infer an omniscient or omnipotent being from the order or mathematical precision inherant and demonstrated in nature.

The fact that pi is equal to pi anywhere in the [known] universe is hardly a wonderous fact, but rather the standard result of fixed variables (in relation to each other) appied against fixed operations producing a fixed result. pi is no more significant than 2+2=4. In fact, if 2+2<>4 then this would be significant of something!

People may point to a cyclone or tornado for instance as a wonderful example of "balance" in the forces of nature or the "perfect" distance that the earth is from the sun or its axis and spin etc. But the resultants e.g. pi, 4, tornados, life-capable planets, are the natural consequences of conditions consistent with their production. 3+5 can never equal 4, Pluto cannot sustain life, some planets spin too fast and are in the wrong place to support life.

As Clarance Darrow said:

The 'implication' of order or "wondrous" mathematical certainties and/or consistencies is actually an assumpion:

"To say that a certain scheme or process shows order or system, one must have some norm or pattern by which to determine whether the matter concerned shows any design or order. We have a norm, a pattern, and that is the universe itself, from which we fashion our ideas. We have observed this universe and its operation and we call it order. To say that the universe is patterned on order is to say that the universe is patterned on the universe. It can mean nothing else." :notworthy

[Clifford Greenblatt]

Originally quoted by Howard
You don't think there's a pretty big stretch from an interesting mathematical concept to a sentient, all powerful being? This kind of gigantic inferential leap reminds me of New Agers latching onto Quantum Mechanical phenomena and using them to justify whatever brand of mysticism they are trying to sell - trance channeling, crystal healing, astrology, etc.. "See," they say, "If that's true then this could be true, too." Could be, yes, but it's little more than imaginative speculation.

These comments and similar comments made by others that followed indicate a failure to understand the scope and purpose of my argument. I was by no means claiming some mathematical facts prove that the Bible is right. My purpose was to counter any claim that the attribute of omnipresence lacks any observable support. Also, I am not claiming that anything that is omnipresent is God. I certainly do not equate God with 2 + 2 = 4, although that equation is an omnipresent fact. I will say that reality is filled with an enormous amount of variety, but some things are omnipresent and immutable.

Consider this conversation between Person A and Person B.

Person A: What kind of work do you do?
Person B: I work for a construction company. We build houses.
Person A: Really? What did you do today?
Person B: I painted some walls.
Person A: You obviously don't know a thing about building a house! Why don't you quit trying to fool people with your outrageous claims! Do you suppose that you can construct an entire house out of can of paint? I once saw some children piling up sand on a beach. They told me that they were building a castle. I doubt they have ever seen any of the great castles of Europe. If they had, they would have known that there is a lot more to building a castle than piling up a few grains of sand. You are no different. You think you can go around with a little paint can and a brush and kablaam– a house! Why don't you stop wasting your life away in pipe dreams and get yourself a real job!
Person B: When did I tell you that I build entire houses all by myself? I am part of a large construction team. I do not paint houses into existence, but my painting is an essential part of the work of the team.

My point in the above dialogue is that there is a very large team of gifted people defending Biblical claims. I did not propose to do the whole job with a single and simple observation about the attribute of omnipresence, but some have apparently made the gigantic inferential leap to the conclusion that this is exactly what I was claiming to do.

The home construction illustration is not meant to be taken to the point of implying that there is a team of Biblical scholars in the world that has a complete proof of the Biblical God. It is meant to illustrate that certain contributions can be very valuable and significant even if they are only a tiny part of the whole picture. Furthermore, theology does not require sufficient scholarship to put together a complete proof of all Biblical claims in order to be a valid discipline. This is well understood in scientific disciplines. Science is not made invalid by the failure of present day scientists to have a complete theory of reality. As in any other discipline, there will be plenty of incompetent or misguided individuals making erroneous claims in theology. This too does not invalidate the discipline of theology.

[Howard]

Well, Clifford this is the Existence of God forum so it is not unreasonable to presume that your OP was connected with that topic. Besides, most of us are hungry for fresh theists with fresh arguments, so you’ll have to forgive us if we tend to pounce a bit too enthusiastically.

If your point is that “omnipresence” is, at least in the mathematical world, a supportable concept, okay I guess, but you still have a long way to go. As for “a very large team of gifted people defending Biblical claims” let us not forget that similar teams of people defended geo-centricity claims for much of Christian history.

Furthermore, comparing theological claims with scientific claims is not valid… unless you can tell us how to verify (or falsify) them.

And if you have specific Biblical claims you wish to present, there are some very knowledgeable people on that forum who would be thrilled to see you.

I also think we have few housepainters about if that's your interest.

[rainbow walking]

Originally posted by Clifford Greenblatt
These comments and similar comments made by others that followed indicate a failure to understand the scope and purpose of my argument. I was by no means claiming some mathematical facts prove that the Bible is right. My purpose was to counter any claim that the attribute of omnipresence lacks any observable support. Also, I am not claiming that anything that is omnipresent is God. I certainly do not equate God with 2 + 2 = 4, although that equation is an omnipresent fact. I will say that reality is filled with an enormous amount of variety, but some things are omnipresent and immutable.

rw: Okay, three dimensional space is an omnipresent coordinate from which some immutable equations emerge. This is only trivially true and would have to be the case for a logical space/time universe to exist where sentient creatures could arise and develop the capability of abstract symbolic reasoning. Why call this omnipresent? Intrinsic would be a more accurate term. These foundational principles of our reality are intrinsic to a logical space/time coordination of matter and nothing more. I fail to see how this correlates to an omnimax god except that an attribute is shared if you don't press for accuracy in term designation.

Consider this conversation between Person A and Person B.

Person A: What kind of work do you do?
Person B: I work for a construction company. We build houses.
Person A: Really? What did you do today?
Person B: I painted some walls.
Person A: You obviously don't know a thing about building a house! Why don't you quit trying to fool people with your outrageous claims! Do you suppose that you can construct an entire house out of can of paint? I once saw some children piling up sand on a beach. They told me that they were building a castle. I doubt they have ever seen any of the great castles of Europe. If they had, they would have known that there is a lot more to building a castle than piling up a few grains of sand. You are no different. You think you can go around with a little paint can and a brush and kablaam– a house! Why don't you stop wasting your life away in pipe dreams and get yourself a real job!
Person B: When did I tell you that I build entire houses all by myself? I am part of a large construction team. I do not paint houses into existence, but my painting is an essential part of the work of the team.

My point in the above dialogue is that there is a very large team of gifted people defending Biblical claims. I did not propose to do the whole job with a single and simple observation about the attribute of omnipresence, but some have apparently made the gigantic inferential leap to the conclusion that this is exactly what I was claiming to do.

rw: I see no leap in calling a spade a spade. No one appeared to me to be assuming you were offering this as a do-all-end-all proof that a god exists. Instead I see replies correctly zeroed in on the inference you are drawing in the comparison. That the example fails to make any solid connection with an isolated, scarcely debated attribute often tossed into the definition of the christian god, is no reason to start packing to move into a newly constructed house whose walls are being constructed from analogies. I doubt anyone sceptical of such claims will find much solace from the elements while standing beneath a mathematical equation.

The home construction illustration is not meant to be taken to the point of implying that there is a team of Biblical scholars in the world that has a complete proof of the Biblical God. It is meant to illustrate that certain contributions can be very valuable and significant even if they are only a tiny part of the whole picture. Furthermore, theology does not require sufficient scholarship to put together a complete proof of all Biblical claims in order to be a valid discipline. This is well understood in scientific disciplines. Science is not made invalid by the failure of present day scientists to have a complete theory of reality. As in any other discipline, there will be plenty of incompetent or misguided individuals making erroneous claims in theology. This too does not invalidate the discipline of theology.

rw: Again you seem to be hastening to assure us that you are not really attempting to do what you are really attempting to do. If you find any value or significance in noting how three dimensional space is susceptable to math equations that hold across all constituent points of reality is analogous to one attribute used to define a god, then I wonder if you are equally as credulous about other bizarre claims like the existence of ghosts and how analogous their amazing ability to pass thru walls are with gamma rays?

[hinduwoman]

The whole argument is based on a mathematical model which is an abstract concept. So by analogy, God too becomes an abstract concept --- something that is only in our heads but not present in any concrete fashion.

[Viking]

Originally posted by hinduwoman
The whole argument is based on a mathematical model which is an abstract concept. So by analogy, God too becomes an abstract concept --- something that is only in our heads but not present in any concrete fashion.

That gets right to point, doesn't it? I understand the power of mathematics, but is it not true that mathematical truth only exists in its own limited context? For example, there are no actual straight lines and perfect spheres in material reality, are there? This is a question I have puzzled over with my only admittedly limited brain power.

[Clifford Greenblatt]

Originally quoted by hinduwoman
The whole argument is based on a mathematical model which is an abstract concept. So by analogy, God too becomes an abstract concept --- something that is only in our heads but not present in any concrete fashion.

Originally quoted by Viking
That gets right to point, doesn't it? I understand the power of mathematics, but is it not true that mathematical truth only exists in its own limited context? For example, there are no actual straight lines and perfect spheres in material reality, are there? This is a question I have puzzled over with my only admittedly limited brain power.

Does e = m * c ^ 2 exist in material reality? For that matter, do any of the laws of physics exist in material reality? If no mathematical entities exist in material reality, then why do material things seem to be unable to escape their influence? Would you not agree that a digital computer can exist in material reality? Suppose there is another universe with a different ratio for proton to electron mass. Suppose a digital computer is constructed in that universe. If the sequence of digits that compose the base 10 representation of the square root of 3 is not part of material reality, then why would that computer produce exactly the same sequence of digits as a computer in this universe when computing it? (Notice that I avoided using pi in this illustration to avoid a great deal of irrelevant controversy)

[rainbow walking]

Originally posted by Clifford Greenblatt
Does e = m * c ^ 2 exist in material reality? For that matter, do any of the laws of physics exist in material reality? If no mathematical entities exist in material reality, then why do material things seem to be unable to escape their influence? Would you not agree that a digital computer can exist in material reality? Suppose there is another universe with a different ratio for proton to electron mass. Suppose a digital computer is constructed in that universe. If the sequence of digits that compose the base 10 representation of the square root of 3 is not part of material reality, then why would that computer produce exactly the same sequence of digits as a computer in this universe when computing it? (Notice that I avoided using pi in this illustration to avoid a great deal of irrelevant controversy)

rw: The symbols exist in physical reality as you can plainly see. The symbols are equivalent to some material phenomenon in physical reality if we all agree to those symbols being acceptable representations. Are the symbols the literal physical phenomenon they represent? Not at all. That we can symbolize abstract physical properties of our material existence doesn't fall out as being equivalent to biblical symbolisms having equal or greater equivalence to physical or material reality. That there are some parallels is not equivalent to both being equally valid symbolics of real phenomena.

General relativity has proven to be a relaible link in a chain of human knowledge about our physical reality that has facilitated an increased understanding of many of the underlying properties of that material reality and how they are inter-connected.

At best, biblical symbolics have affirmed some psychological patterns in humanity that amount to inter-connected human behaviors from a normative value perspective. Translating these truths to mean a god exists who created physical reality does not follow. At some point there is an unjustified leap of faith. I say unjustified while you are likely to disagree. So perhaps the issue is a matter of justifying the leap of faith.

Comparing the construction of a digital computer is not analogous to a being who created all existent things. So my burden of justification for the digital computer isn't as great as a burden for the justification of an omnimax god. Every step of ground I have to cover to justify my reliance on the symbolics of math to get me to a digital computer is verifiable. The same cannot be said for justifying every step a theist must make to get from human's being capable of right and wrong to an existent creator deity as verifiable. There is a greater leap, the gulf is wider and the space between dis-connected. At some point the theist has to let go of his grip on rational threads and trust his momentum to carry him the remainder of the way across the gulf.

[rainbow walking]

Originally posted by rainbow walking
rw: The symbols exist in physical reality as you can plainly see. The symbols are equivalent to some material phenomenon in physical reality if we all agree to those symbols being acceptable representations. Are the symbols the literal physical phenomenon they represent? Not at all. That we can symbolize abstract physical properties of our material existence doesn't fall out as being equivalent to biblical symbolisms having equal or greater equivalence to physical or material reality. That there are some parallels is not equivalent to both being equally valid symbolics of real phenomena.

General relativity has proven to be a relaible link in a chain of human knowledge about our physical reality that has facilitated an increased understanding of many of the underlying properties of that material reality and how they are inter-connected.

At best, biblical symbolics have affirmed some psychological patterns in humanity that amount to inter-connected human behaviors from a normative value perspective. Translating these truths to mean a god exists who created physical reality does not follow. At some point there is an unjustified leap of faith. I say unjustified while you are likely to disagree. So perhaps the issue is a matter of justifying the leap of faith.

Comparing the construction of a digital computer is not analogous to a being who created all existent things. So my burden of justification for the digital computer isn't as great as a burden for the justification of an omnimax god. Every step of ground I have to cover to justify my reliance on the symbolics of math to get me to a digital computer is verifiable. The same cannot be said for justifying every step a theist must make to get from human's being capable of right and wrong to an existent creator deity as verifiable. There is a greater leap, the gulf is wider and the space between dis-connected. At some point the theist has to let go of his grip on rational threads and trust his momentum to carry him the remainder of the way across the gulf.

rw: Using the above metaphor of leaping across a gulf, when the theist makes this leap does he land in a different world where milk and honey magically flows from rocks upon request; where diseases dry up and vanish or men walk on water at will or command storms to cease and desist?

No, he does not. He comes down in exactly the same place from whence he lept with only this one difference...he is now convinced that this world is also capable of being that other world if only his faith aligns with a gods will to make it so. All that has changed is his perspective of this world. So is that perspective justified? Can he draw a direct path from his leap to a miacle we can all agree on as having its origins in another realm? This has not been demonstrated and is also a matter of faith based on interpretation. That some things will happen in his life that seem inexplicable otherwise he will not deny, nor consider any other explanation. His leap of faith has netted him a conviction that some things about this world are inexplicable sans his appeal to a god and supernature. It amounts to an additional interpretative paradigm inter-woven into his basic interpretative faculties. How thoroughly he applies it to his circumstances is subjectively determined by the strength of his conviction of its truth. Not all convictions are held equally by all who are so convicted. I would say this accounts for the spectrum of biblical interpretations and doctrines and their variety as well as dogmatic status. I would also say this holds true across all religious belief and faiths regardless of the deity to whom they are attributed.

So what initially inspired or compelled him to make this leap?

[HRG]

Originally posted by Clifford Greenblatt
Does e = m * c ^ 2 exist in material reality?

Yes - as a pattern of ink on paper in physics textbooks.

For that matter, do any of the laws of physics exist in material reality? If no mathematical entities exist in material reality, then why do material things seem to be unable to escape their influence?

IMHO you put the cart before the horse. Material things behave in a certain way, and we describe and explain this behavior. We call this description/explanation the "laws of physics, chemistry ...". IOW, behavior comes first, our description second.

And of course, there is the big difference between reality and our approximate mathematical models of reality. Real planets do not move in ellipses.

Would you not agree that a digital computer can exist in material reality? Suppose there is another universe with a different ratio for proton to electron mass. Suppose a digital computer is constructed in that universe. If the sequence of digits that compose the base 10 representation of the square root of 3 is not part of material reality, then why would that computer produce exactly the same sequence of digits as a computer in this universe when computing it?

Because it would be programmed with exactly the same algorithm in order to produce the digits of sqrt(3).

In any case, you would only find an approximation to sqrt(3) within this universe (digital computers are finite), and you would need an intelligent being to make the link between the states of some memory cells and the digital representation of sqrt(3). The states of the memory cells by themselves do not contain sqrt(3).

regards,
HRG.

[Clifford Greenblatt]

Originally posted by HRG
Because it would be programmed with exactly the same algorithm in order to produce the digits of sqrt(3).

The algorithm does not have to be exactly the same. There are generally various algorithms that can be used to produce the same result. Also, whether or not the algorithm is identical, the programmer does not need to have any knowledge of the actual digits to write the algorithm to produce the digits. The sequence of digits is infinite and nonperiodic.

Originally posted by HRG
In any case, you would only find an approximation to sqrt(3) within this universe (digital computers are finite), and you would need an intelligent being to make the link between the states of some memory cells and the digital representation of sqrt(3). The states of the memory cells by themselves do not contain sqrt(3).

The sequence of digits is the same whether or not anyone observes them. The digits do not need to be stored in any memory cells. They could be output sequentially on a display, one digit at time. Although a machine can output only a finite number of digits in a finite amount of time, the length can be arbitrarily large. If a computer in one universe outputs 10 ^ 12 digits and a computer in another universe outputs 10 ^ 12 digits, and if neither computer malfunctions, then both sequences of 10 ^ 12 digits will be identical.

[Viking]

Originally posted by Clifford Greenblatt
Does e = m * c ^ 2 exist in material reality? For that matter, do any of the laws of physics exist in material reality? If no mathematical entities exist in material reality, then why do material things seem to be unable to escape their influence? Would you not agree that a digital computer can exist in material reality? Suppose there is another universe with a different ratio for proton to electron mass. Suppose a digital computer is constructed in that universe. If the sequence of digits that compose the base 10 representation of the square root of 3 is not part of material reality, then why would that computer produce exactly the same sequence of digits as a computer in this universe when computing it? (Notice that I avoided using pi in this illustration to avoid a great deal of irrelevant controversy)

I do not think material things are influenced at all by the mathematical constructs that model them, approximate them or whatever. I fully accept that the universe operates with a high degree of predictability, however, but we also know that at the quantum level there is very little certainty. The fact that a digital computer constructed in another universe would produce exactly the same sequence of digits for the base 10 represenatation of the square root of 3 is begging the question. A sausage maker in another universe would also produce sausage if the right ingredients were added. I just don't see what the exisitence of machine programmed to calculate symbols performing as designed has to do with the fabric of reality.

[Ellis14]

I don't agree, unless we're going to say that another universe has different laws of physics and maths that ours does, in which case, what's the point of this argument?

It doesn't matter whether there is some abstracted force are transcendant relative understanding or framework behind numbers, digits, operations and calculations. There might be, but they are irrelevant in understanding the operation and result:

If you put a figure, eg: 2 in a computer and drop another one in, eg 5. Use the same operator, i.e: X and then calculate the result correctly, the resultant value is: 10. This will work no matter what computer you use in any part of the universe, ever. Not because the concepts of numbers or computers are universal, or because space-time works in a special ways on planet earth than it does elsewhere, but because numbers, factors, operators and calculations are based on mathematical principles consistent with the universe itself: (We build our maths around the universe, not the other way around.)

To say that anything else is possible is to reject all experience and understanding of the universe. If the universe is not consistent then anything could result in anything, but it doesn't; the same figures produce the same results, everytime. What does this show?

[Clifford Greenblatt]

Originally posted by Viking
I do not think material things are influenced at all by the mathematical constructs that model them, approximate them or whatever. I fully accept that the universe operates with a high degree of predictability, however, but we also know that at the quantum level there is very little certainty. The fact that a digital computer constructed in another universe would produce exactly the same sequence of digits for the base 10 represenatation of the square root of 3 is begging the question. A sausage maker in another universe would also produce sausage if the right ingredients were added. I just don't see what the exisitence of machine programmed to calculate symbols performing as designed has to do with the fabric of reality.

The mathematical constructs are in the mind, pen and ink, etc., but they are a direct consequence of the mathematical principles that are intrinsic to all of material reality and which are absolutely invariant. The uncertainties of quantum mechanics could be taken too far. These uncertainties limit our ability to measure things like position and momentum and they allow a great deal of freedom, but that freedom exists within a framework of some fundamental principles which are common to all of reality and which are absolutely invariant. If a sausage maker could exist in another universe, the sausage made by that sausage maker would never be identical to any sausage made in this universe. In fact, the same cook could never make two absolutely identical sausages in same hour, in the same kitchen, with identical twin pigs. On the other hand, the sequence of digits representing the square root of three in base ten would be absolutely identical in all universes.

[Howard]

Originally posted by Clifford Greenblatt
In fact, the same cook could never make two absolutely identical sausages in same hour, in the same kitchen, with identical twin pigs. On the other hand, the sequence of digits representing the square root of three in base ten would be absolutely identical in all universes. Yes, but that’s only because you have defined both numbers and the square root operation in a specific way. The axioms of logic, such as non-contradiction and the excluded middle, would also be invariant, but only because they are defined that way.

I could also define an operator called “##” such that: 2##2 = 5. That too, would be invariant in all universes, but so what?

Again, I don’t see how any of this implies anything god-like about this or any other universe.

[HRG]

Originally posted by Clifford Greenblatt , in part:



The sequence of digits is the same whether or not anyone observes them.

There is no sequence of digits, only a pattern of charges in a semiconductor. We need someone to interpret it as a sequence of digits.

The digits do not need to be stored in any memory cells. They could be output sequentially on a display, one digit at time.

You mean that a pattern of light spots can appear sequentially on a display. As before, we need someone to interpret them as an output of digits.

Regards,
HRG.

[Clifford Greenblatt]

Originally posted by Howard
Yes, but that's only because you have defined both numbers and the square root operation in a specific way. The axioms of logic, such as non-contradiction and the excluded middle, would also be invariant, but only because they are defined that way.
I could also define an operator called "##" such that: 2##2 = 5. That too, would be invariant in all universes, but so what?

The infinite sequence of digits that represent the square root of three in base ten goes far beyond simple definition because those digits are infinite in number and nonperiodic. Of course one could choose a number with six digits, such as 3.14159, and it would be trivially invariant in all universes by definition. The finite amount of information that defines the square root of three may be invariant by definition, but the invariance of the infinite and nonperiodic sequence of digits in its decimal representation is not simply a matter of definition but is a consequence of intrinsic and invariant properties of reality.

[Howard]

There has been a great deal of discussion here on the relationship between mathematics and physical reality. Some believe mathematics is an intrinsic part of nature while others believe it is purely a human construct that is highly useful in our understanding of nature. Count me in the second group.

So like the soundless tree that falls in the forest if there is no living being to hear it, your “infinite sequence of digits that represent the square root of three in base ten” does not physically exist without a human to compute it - after first defining numbers, bases and the square root operation.

[Clifford Greenblatt]

Originally posted by Howard
So like the soundless tree that falls in the forest if there is no living being to hear it, your "infinite sequence of digits that represent the square root of three in base ten" does not physically exist without a human to compute it - after first defining numbers, bases and the square root operation.

This seems similar to the mystical Copenhagen Interpretation of quantum mechanics in which a wave function collapses when a conscious observer detects it. It also seems similar to the New Age idea that the universe came into being in anticipation of the future existence of conscious beings. Are you saying that nothing exists until a conscious observer detects it?

[Howard]

Not at all. I believe in an objective reality that exists independent of human experience and interaction. I’m just not convinced that the square root of three exists without a conscious intelligence to define it.

[Clifford Greenblatt]

Originally posted by Howard
Not at all. I believe in an objective reality that exists independent of human experience and interaction. I'm just not convinced that the square root of three exists without a conscious intelligence to define it.

Definitions, descriptions, and instructions help connect us to things in objective reality. If I were to describe a Blogg to you as a frog which is as big as a giraffe, has a large eye in the middle of its head, and may be found in Neverland, this would not help connect you with anything in objective reality. If I describe a real elephant to you and to another person and name a real zoo at which it is located, then both of you would be connected with the exact same item in objective reality. If the description is at all useful, neither of you would be looking for a chimpanzee. If you visit the elephant, you would be observing photons which bounced off the elephant and into your eyes. The physical elephant itself would not be entering into your mind, but a neural representation of it would. If I give you a programme for computing the decimal representation of the square root of three to as many decimal places as your computer is capable of handling, then I would be connecting you with something that exists in objective reality which has infinite complexity. You could not explore the entirety of this infinitely complex thing because it is much too large for either you or your computer to handle. However, to the extent that you can explore it, it will be identical to the decimal representation of the square root of three that another person would be exploring on another computer.

[Ellis14]

Definitions, descriptions, and instructions help connect us to things in objective reality. If I were to describe a Blogg to you as a frog which is as big as a giraffe, has a large eye in the middle of its head, and may be found in Neverland, this would not help connect you with anything in objective reality. If I describe a real elephant to you and to another person and name a real zoo at which it is located, then both of you would be connected with the exact same item in objective reality. If the description is at all useful, neither of you would be looking for a chimpanzee. If you visit the elephant, you would be observing photons which bounced off the elephant and into your eyes. The physical elephant itself would not be entering into your mind, but a neural representation of it would. If I give you a programme for computing the decimal representation of the square root of three to as many decimal places as your computer is capable of handling, then I would be connecting you with something that exists in objective reality which has infinite complexity. You could not explore the entirety of this infinitely complex thing because it is much too large for either you or your computer to handle. However, to the extent that you can explore it, it will be identical to the decimal representation of the square root of three that another person would be exploring on another computer.

Exactly. :notworthy