Do Mathematical Entities Really Exist?

[AgingYoung]

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. .....hardcore math dude

Gene

eta: whether we or some beaver knows there is a distinct ratio between the circumference of a circle to its diameter and is the same for all circles or that similar parts of similar triangles are in proportion or any other sort of relationship in time and space that relationship exists. The math we use to describe some relationships might not be accurate but the relationships are very real, imo, and exist in spite of our inaccurate descriptions of them or even of our outright ignorance of them.

 

[ynot]

If anyone claims that math is an entity (has actual existence), I would like them to give an actual existence example of absolute zero (or of a negative value)

 

[AgingYoung]

I think I see your point, Ynot. You're saying that since some (theoretical) relationships don't exist (ie absolute zero) no actual, real relationship has a right to exist. Is that your point? Sort of like equal rights for relationships?

Gene

 

[BPScooter]

My guess on the burger ad would be something like:
FDA tells us we can't label anything as "Beef" unless it contains x/y percent beef meat, from certain cuts.
We want to push the limit and deceive the public to maximize tasty sales.
Hence, we have put the legally allowable amount of minimum beef.

Now they have to play the same game with trans fats (NYC has sent the message, deep fryers beware).

Less math than marketing, from my first glimpse of that example.

 

[Zygar]

If anyone claims that math is an entity (has actual existence), I would like them to give an actual existence example of absolute zero (or of a negative value)

I don't think anyone believes math is an entity. We are arguing of the existence of mathematical entities. Quite a different subject.

As for zero and negative values, zero is clearly an abstract concept. Being defined as the absence of something, it is quite non-existent. Negatives could exist in the form of vectors. Perhaps the force of gravity or friction or air resistance. I hadn't really given much thought to negatives specifically.

 

[delphi_ote]

Negatives could exist in the form of vectors. Perhaps the force of gravity or friction or air resistance. I hadn't really given much thought to negatives specifically.

I can have a negative account balance. Is the concept of owing someone real? I'm inclined to think not, but this conversation brings up all kinds of interesting questions. I approve.

 

[Kaylee]

I can have a negative account balance. Is the concept of owing someone real?

Your banker probably thinks so.

Good thread! I had always thought of mathematics as an objective area of study, and so I'm surprised at how differently one can intrepret it's entities to mean. But, perhaps I shouldn't be. IANAM, but it seems that among other things, mathematics is a tool to help us manipulate the "patterns" we become aware of, directly or indirectly, in the universe around us. How we regard these patterns and the tools we use to manipulate them is, it seems, based on this thread, a very subjective affair.

 

[tsig]

Sorry. I merged the statements and ended up with humanity in the noise question.

I still see this as a arrogant and naive view of the issue. Humans hear through an entirely seperate mechanism from ants, sharks, and many other creatures. Also their nervous systems are often completely different from our own. They most likely do not percieve sound as we do. But just because an observer with ears is not present, doesn't mean the noise is not present.

Agreed, they are different. But "two pianos" are a specific form of two which require the existance of the mathematical entity "two". The number doesn't have to be understood to be present.

Beauty and pi are unrelated. Beauty is relative, pi is absolute. Two people cannot agree on what is beautiful, so aliens are guaranteed to never agree. On the other hand pi can be agreed upon by any two individuals on earth, even without speaking a similar language. Aliens will also agree on the value of pi, even if it is in a different base. If the value can be arrived at independently by any intelligent race, is it not real?

I support nimzov's take on this.

To the animal that died under the tree, it fell.

Let's all have a moment of silence.

 

[ynot]

I think I see your point, Ynot. You're saying that since some (theoretical) relationships don't exist (ie absolute zero) no actual, real relationship has a right to exist. Is that your point? Sort of like equal rights for relationships?

Gene

Well let's face it, relationships don't really work anyway. The inevitable compromises involved just eat away at ones individuality. Do relationships actually exist, or are they just abstract concepts? How do we exactly define the parameters of the things we are relating?

 

[ynot]

I don't think anyone believes math is an entity. We are arguing of the existence of mathematical entities. Quite a different subject.

As for zero and negative values, zero is clearly an abstract concept. Being defined as the absence of something, it is quite non-existent. Negatives could exist in the form of vectors. Perhaps the force of gravity or friction or air resistance. I hadn't really given much thought to negatives specifically.

If we agree that absolute zero can't actually exist, then it must follow that actual existence is a contiguous, single entity (still a singularity . Any division of existence therefore is an abstract exercise.

 

[Zygar]

If we agree that absolute zero can't actually exist, then it must follow that actual existence is a contiguous, single entity (still a singularity . Any division of existence therefore is an abstract exercise.

Ha! I opened myself up to this one.

I think I'll just retract this statement since I am not a philospher and I don't really know enough about the differing views of reality to enter this discussion from this context.

 

[ttias]

I don't know about math (acctually I do, but I don't know english well enough to express myself coherently), but... In Sweden you can buy sausages with 129% meat in them. Or so they claim.

Allthough I don't seem to be able to post links as of yet... I'll be back with my source later on.

 

[ynot]

I don't know about math (acctually I do, but I don't know english well enough to express myself coherently), but... In Sweden you can buy sausages with 129% meat in them. Or so they claim.

Allthough I don't seem to be able to post links as of yet... I'll be back with my source later on.

Advertisers have a habit of stretching the truth. If you have a whole apple and half an apple, do you have 150% of an apple?

ETA - If an amount is defined (abstractly) as being a whole amount (100%), and that amount is exceeded, then 100%+ is possible according to that definition. I suspect that Swedish authorities define a minimum amount of meat that sausages must contain, and the manufacturer has exceeded that amount by 29%.

 

[AgingYoung]

I don't know about math (acctually I do, but I don't know english well enough to express myself coherently), but... In Sweden you can buy sausages with 129% meat in them. Or so they claim.

Allthough I don't seem to be able to post links as of yet... I'll be back with my source later on.

I've heard in some countries their tax scheme is such that you can owe 120% of your income in taxes. Now sausages too? I'm going to give 150% of my abilities to understand this.

Gene

 

[baron]

I've only skimmed through this thread, but it may be relevant how some calculating savants claim to perform their mathematical feats. Whereas traditional mathematical methods use symbols to represent numbers (i.e. 1, 2, 3...), some prodigies report that they can actually see the "mathematics" and that each number has a distinct visual independent of any external symbolism. These objects interact to form the solution. To my mind, the sheer speed at which these prodigies can calculate suggests they are not processing symbols but may actually be directly accessing the underlying mathematics.

Here's a snippet from an article on Daniel Tammet, one such prodigy (I can't post URLs ATM) ~

Tammet is calculating 377 multiplied by 795. Actually, he isn't "calculating": there is nothing conscious about what he is doing. He arrives at the answer instantly. Since his epileptic fit, he has been able to see numbers as shapes, colours and textures. The number two, for instance, is a motion, and five is a clap of thunder. "When I multiply numbers together, I see two shapes. The image starts to change and evolve, and a third shape emerges. That's the answer. It's mental imagery. It's like maths without having to think."...

Last year Tammet broke the European record for recalling pi, the mathematical constant, to the furthest decimal point. He found it easy, he says, because he didn't even have to "think". To him, pi isn't an abstract set of digits; it's a visual story, a film projected in front of his eyes. He learnt the number forwards and backwards and, last year, spent five hours recalling it in front of an adjudicator. He wanted to prove a point. "I memorised pi to 22,514 decimal places, and I am technically disabled. I just wanted to show people that disability needn't get in the way."

 

[ynot]

I've only skimmed through this thread, but it may be relevant how some calculating savants claim to perform their mathematical feats. Whereas traditional mathematical methods use symbols to represent numbers (i.e. 1, 2, 3...), some prodigies report that they can actually see the "mathematics" and that each number has a distinct visual independent of any external symbolism. These objects interact to form the solution. To my mind, the sheer speed at which these prodigies can calculate suggests they are not processing symbols but may actually be directly accessing the underlying mathematics.

Here's a snippet from an article on Daniel Tammet, one such prodigy (I can't post URLs ATM) ~

I've also seen a TV program where "normal" people could perform amazing maths by visualising that they were using an abacus then they simply "see" the results.

ETA - I wonder if Tammet could draw the shapes he sees so they could be analysed.

 

[ynot]

I was going to see if I could devise such a system, but I think I'll just wait for the Kevin Trudeau book

 

[nimzov]

I've only skimmed through this thread, but it may be relevant how some calculating savants claim to perform their mathematical feats. Whereas traditional mathematical methods use symbols to represent numbers (i.e. 1, 2, 3...), some prodigies report that they can actually see the "mathematics" and that each number has a distinct visual independent of any external symbolism. These objects interact to form the solution. To my mind, the sheer speed at which these prodigies can calculate suggests they are not processing symbols but may actually be directly accessing the underlying mathematics.

Here's a snippet from an article on Daniel Tammet, one such prodigy (I can't post URLs ATM) ~

Tammet is calculating 377 multiplied by 795. Actually, he isn't "calculating": there is nothing conscious about what he is doing. He arrives at the answer instantly. Since his epileptic fit, he has been able to see numbers as shapes, colours and textures.

According to this list Tammet is number five for the record.

The first four are not savants.

What method do they use ?

nimzo

 

[baron]

According to this list Tammet is number five for the record.

The first four are not savants.

What method do they use ?

Memory, I would assume. The reason I quoted Tammet is that he doesn't memorise symbols, he "sees" the numbers' form. And I don't think coming 5th has any significance as I understand he did it to prove a point, as stated, and didn't simply give up on account of digit 25515 slipping his mind.

In any event, that's not the point. The point is that calculating savants do not deal with symbols, they use some other method which is as yet unexplained. Let's not confuse that with sad people who spend their lives memorising Pi.

 

[Kaylee]

What an interesting derail! How about this for a theory?

Tammet may be experiencing synesthesia.

(See http://web.mit.edu/synesthesia/www/
and http://psyche.cs.monash.edu.au/v2/psyche-2-10-cytowic.html

In the second link read paragraphs 2.8

Not only do most synesthetes contend that their memories are excellent, but cite their parallel sensations as the cause, saying for example, "I know it's 2 because it's white." Conversation, prose passages, movie dialogue, and verbal instructions are typical subjects of detailed recall. The spatial location of objects is also strikingly remembered, such as the precise location of kitchen utensils, furniture arrangements and floor plans, books on shelves, or text blocks in a specific book.

and paragraph 4.10

Synesthesia is memorable. At first, we are impressed by synesthetes' excellent figurative memory and taken with their anecdotes of how the "extra bits" help them to remember telephone numbers, appointments, and the like. It was Luria's The Mind of A Mnemonist (1968) that first suggested to me a link between synesthesia and hypermnesis. The apparently limitless memory of his subject, S, seemed due to the synesthesiae that accompanied his every experience. During recall, S described a replay of somatic feelings and "an overall sensation" during which "the thing remembers itself."

)

There are people who have blind sight and the equivalent in hearing (although to the best of my knowledge it's not called deaf hearing). In other words, some people see or hear on an unconscious level that never becomes conscious.

(For more on blindsight see http://serendip.brynmawr.edu/bb/blindsight.html)

Following certain kinds of brain lesions, patients report an inability to see objects, but if pressed to guess at their location they display a capacity to point at them with reasonable accuracy. The phenomenon, called "blindsight", is one of the more dramatic of a number of lines of evidence suggesting that being aware of doing something is distinguishable from doing something, that areas of the brain underlying the experience of doing at least some things are distinct from those needed to actually do those things.

Such a dissociation has a number of interesting implications. In a general sense, it provides evidence for the existence and significance of an "unconscious" as a contributor to human behavior (and hence for "consciousness" as distinctive part rather than synomous with the totality of brain function).

)

So, perhaps as a result of an epileptic fit, he became partially brain damaged although it seems in his case it could be fair to say brain enhanced ?

Perhaps he lost the ability to consciously perform math calculations, but can still perform them unconsciously. While doing so unconsciously, he experiences synesthesia. A side effect of all this is that he can perform calculations more quickly and "retain" the answer better (in the case of pi he can retain what the quotient is into the 22 thousands plus decimal place.)